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This work aims to look into the dynamic research of coupled NLS-type equations with three components. The optical solitons, including the periodic function, trigonometric function, exponential function, solitary wave, and elliptic function solutions are built using the Jacobi elliptic function (JEF) method. The investigations will aid in improving comprehension of the soliton dynamics system's overall illustration. Using Mathematica software, we visually represent some solutions found in 3D, contour, and 2D graphs for tangible demonstration and visual presentation. These results are helpful in optical fiber, signal processing and data transmission. [ABSTRACT FROM AUTHOR]

This research used a modified and extended auxiliary mapping method to examine the optical soliton solutions of the truncated time M-fractional paraxial wave equation. We employed the truncated time M-fractional derivative to eliminate the fractional order in the governing model. The few optical wave examples of the paraxial wave condition can assume an insignificant part in depicting the elements of optical soliton arrangements in optics and photonics for the investigation of different actual cycles, including the engendering of light through optical frameworks like focal points, mirrors, and fiber optics. We identified the solution using a few free parameters regarding hyperbolic function form. We discovered periodic wave, bright and dark kink wave, bell wave, and singular soliton solution for the numerical values of the free parameters. To explain the behavior of various solutions, we have spoken the obtained solutions graphically for a physical explanation using MATLAB. The strategy introduced is fundamental and robust as a smart soliton solution for nonlinear partial differential equations, and it may play a crucial role in nonlinear optics, fiber optics, and communication systems. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to provide the optical solitons of the twin-core couplers with optical metamaterials having Kudryashov's sextic power law of arbitrary refractive index. The trial equation method and the complete discrimination system for polynomial are used to find exact solutions for a broad variety of optical solitons. Additionally, we analyze the topological stability of these patterns to investigate whether the forms of the solutions change when the parameters are perturbed, as a way to show the effect on the model when the parameters are changed. [ABSTRACT FROM AUTHOR]

This study offers a comprehensive analysis of the Perturbed Schrödinger -Hirota Equation (PSHE), crucial for understanding soliton dynamics in modern optical communication systems. We extended the traditional Nonlinear Schrödinger Equation (NLSE) to include higher-order nonlinearities and spatiotemporal dispersion, capturing the complexities of light pulse propagation. Employing the modified auxiliary equation method and Adomian Decomposition Method (ADM), we derived a spectrum of exact traveling wave solutions, encompassing exponential, rational, trigonometric, and hyperbolic functions. These solutions provide insights into soliton behaviors across diverse parameters, essential for optimizing fiber optic systems. The precision of our analytical solutions was validated through numerical solutions, and we explored modulation instability, revealing conditions for soliton formation and evolution. The findings have significant implications for the design and optimization of next-generation optical communication technologies. [ABSTRACT FROM AUTHOR]

The Schrödinger model, which describes the mobility of a single wave in an optical fiber, is crucial to communication systems. By using the quadrupled-power law and the dual form of nonlocal nonlinearity, this study concentrates on establishing optical solitary solutions for Kudryashov’s law of nonlinear refractive index. The unified Riccati equation method and the new extended auxiliary equation approach are used to derive numerous ranges of Jacobi elliptic, trigonometric, hyperbolic, and dual-wave solitary solution patterns. These findings will eventually lead to the discovery of bright, singular, kink, dark–bright, and singular-periodic soliton solutions, whose 3D, 2D, and density depictions are provided with the help of mathematical software, Mathematica. Moreover, we provide 2D graphical representations for different values of the fractional and time parameters to show how these novel optical solutions behave. Different features of these solitons arise in many physical contexts such as nonlinear optics, fluid dynamics, and laser physics. The derived results show that the proposed framework presents a rich and varied spectrum of wave phenomena and that the methods for solving nonlinear partial differential equations arising in mathematical physics are effective, useful, and dependable for further exploration in the vast field of optical and mathematical physics. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation describes a wide spectrum of non-linear wave phenomena across different fields of physics and engineering, including optical pulse transmission, propagation of intense light pulses, soliton propagation, quantum optics, self-phase modulation, dynamics of ultra-cold atomic gases, non-linear dynamics of plasma waves, dynamics of wave packets, quantum information theory, etc. In this study, we investigate the higher-order non-linear Schrödinger equation (hNLSE) and the perturbed non-linear Schrödinger equation (pNLSE) with Kerr law non-linearity by using a conformable and reliable expansion scheme. The solutions are constructed in terms of transcendental functions, specifically the exponential and trigonometric functions, and their dynamics are explained through two-, three-dimensional, and contour plots using the symbolic computation software Mathematica for certain parameter values, exhibiting soliton characteristics within the defined ranges. The solutions exhibit distinct soliton characteristics, like kink-shaped, one-sided kink-shaped, anti-bell-shaped, parabolic-shaped, and others. The solutions attained are compared with those documented in the existing literature, which highlights their originality. The obtained soliton solutions hold potential for theoretical analysis of soliton propagation, non-linear dynamics of plasma waves and ultra-cold atomic gases, communications through optical fiber, etc. [ABSTRACT FROM AUTHOR]

In dispersion oscillating fiber, various optical wave patterns attained for inhomogeneous NLS equation with parabolic tapered profile. With the presence of tapered function, variable coefficient nonlinear Schrödinger equation is considered. Especially, parabolic tapered profile is adopted to tapered function. Numerous optical soliton wave patterns attained for periodically oscillating dispersion profiles. The group of nonlinear optical wave patterns obtained in the present work are useful for control and management of optical waves in nonlinear tapered fiber medium. Moreover, these results are might be helpful in understanding of optical solitons in dispersion oscillating fiber more deeply. [ABSTRACT FROM AUTHOR]

This paper introduces a new controllable anomalous hollow cosh-Gaussian beam (CAHcGB). Based on the Snyder-Michell model and the ABCD matrix description of strongly nonlocal nonlinear media (SNNM), we investigate the transmission characteristics of CAHcGB. Analytical expressions for the electric field, beam width, wavefront curvature radius, and critical power of CAHcGB in SNNM are derived. The results demonstrate that CAHcGB undergoes periodic evolution during transmission in SNNM, influenced by both the beam parameters and the initial beam power. When the critical power equals the incident power, the beam width remains unchanged throughout transmission, resembling a CAHcGB soliton; otherwise, it periodically changes, akin to a breather. The study also reveals that the on-axis intensity evolution curve can exhibit various shapes such as concave, platform, or Gaussian-like, depending on the input power. The research results hold significant potential for applications in optical fiber communication systems, all-optical networks, and optical switches. [ABSTRACT FROM AUTHOR]

This paper investigates new analytical wave solutions for the fractional Kuralay-IIB equations (FK-IIBE), including a new definition of the fractional derivative. This model works in disciplines such as ferromagnetic materials, optical fibers, wave mixing, and nonlinear optics. The integrable motion of space curves can be determined by our governing model. This research holds great importance in the area of optical fibers, exact and analytical solitons solution. The polynomial method’s complete discrimination system (CDSPM) is used to identify a variety of exact and analytical soliton solutions such as periodic, hyperbolic, rational, Jacobian elliptic (JE), and trigonometric functions. Additionally, we also convert the JE function into a solitary wave (SW) solution. To provide a comprehensive understanding of the dynamic aspects of the system, we also address bifurcation points, quasi-periodic behavior, sensitivity analysis, Poincarè maps, time series profile, and critical solution conditions. The research offers straightforward, efficient algorithms that can consistently and effectively address FK-IIBE. Machine learning technologies are also utilized to satisfy the criteria defined by dynamic analysis. Python regression learner tools are used for reverse engineering to analyze the mathematical model’s equilibrium based on parameter intervals and thresholds determined by dynamical analysis. [ABSTRACT FROM AUTHOR]

Stripe solitons (SSs), the special localized wavepackets exhibiting periodic modulations, are identified in condensed matter physics and nonlinear science. Here, giant‐chirp and chirp‐free SSs in all‐fiber lasers are demonstrated composed of single‐mode fiber and polarization‐maintaining fiber. The chirp property of SSs depends on the cavity dispersion while the stripe period relies on the fiber birefringence. Theoretical and numerical results coincide with experimental findings, revealing that the filtering and frequency shift of two vector modes is governed by the mode coupling related to birefringence and the nonlinear coupling induced by the phase modulation, respectively, which disrupts their complementarity and ultimately leads to modulation of the overall spectrum. With the aid of the saturable absorption and cross‐phase modulation effects, the multi‐color pulses synergistically overlap, giving rise to the unique SSs. These results present a simple approach for generating chirp‐controllable SSs in all‐fiber lasers, which is crucial for applications in difference frequency generation and soliton physics. [ABSTRACT FROM AUTHOR]

In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and coupled wave packets in nonlinear optical fibers and describes transverse effects in nonlinear fiber optics. Initially, a complex transformation is used to convert the model into a single Nonlinear Ordinary Differential Equation (NODE), from which hyperbolic, exponential, rational, trigonometric, and rational hyperbolic solutions are produced. In order to better understand the physical dynamics, we offer several 3D, contour, and 2D illustrations for the independent selections of physical parameter values. These illustrations highlight the graphic behaviour of some optical solitons and demonstrate that, under certain constraint conditions, acquired optical solitons lose their stability when they approach an axis and display periodic-axial perturbations, which lead to the generation of optical fractals. As a framework, the generated optical solitons have several useful applications in the field of telecommunications. Furthermore, our suggested RMESEM demonstrates its use by broadening the spectrum of optical soliton solutions, offering important insights into the dynamics of the CNHEs, and suggesting possible applications in the management of nonlinear models. [ABSTRACT FROM AUTHOR]

In this paper, we employ the auxiliary equation method (AEM) to show the leverage of the nearest neighbors hopping and the boson–boson interaction in a zig zag optical lattice on the stressed optical solitons (os) and the Modulation Instability (MI) gain of cold bosonic atoms. The pedestal of the work is set on the continuum approximation of a cold bosonic atoms in a zig zag optical lattice which has demonstrated in detailed in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589]. The results collected have enclosed bright, dark optical solitons and the combined bright-dark and bright-bright optical solitons. Compared the acquired results with Tala-Tebue et al. [Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44], further the os including U-shaped and W-shaped profile have been drop in and the powerful of the nearest neighbors hopping and the boson–boson interaction has been exposed across the spatiotemporal and plot evolution of the bright and dark os. Therewith, the MI bands have been stressed and it is observed some new attitude of the MI gain spectra under the induction of the model parameters. The collected results are new in literature in our knowledge and will improve the previous results acquired in refs. [Tala-Tebue E, Rezazadeh H, Djoufack ZI, et al. Optical solutions of cold bosonic atoms in a zig–zag optical lattice. Opt Quant Electron 53(2021):44; Djoufack ZI, TalaTebue E, FotsaNgafo F, et al. Quantum breathers associated with modulational instability in 1D ultracold boson in optical lattices involving nextnearest neighbor interactions. Optik 164(2018):575–589; Zhao XH, Tian B, Liu DY, et al. Dark solitons interaction for a (2+1)-dimensional nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain. Superlattices Microstruct 100(2016):587–595; Uddin MF, Hafez MG, Hammouch Z, et al. Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness. Waves Random Complex Media 2020. https://doi.org/10.1080/17455030.2020.1722331; Inc M, Aliyu AI, Yusuf A. Optical solitons to the nonlinear Shrdingers equation with spatio-temporal dispersion using complex amplitude ansatz. J Mod Opt 2017;64(21):2273–2280]. [ABSTRACT FROM AUTHOR]

The recently reported compactified hyperboloidal method has found wide use in the numerical computation of quasinormal modes, with implications for fields as diverse as gravitational physics and optics. We extend this intrinsically relativistic method into the non-relativistic domain, demonstrating its use to calculate the quasinormal modes of the Schrodinger equation and solve related bound-state problems. We also describe how to further generalize this method, offering a perspective on the importance of non-relativistic quasinormal modes for the programme of black hole spectroscopy. [ABSTRACT FROM AUTHOR]

In this study, we extract the different kinds of exact wave solutions to the concatenation model, which is a combination of the nonlinear Schrödinger equation, the Lakshmanan-Porsezian-Daniel model, and the Sasa-Satsuma model. We use the unified method to extract new solutions. This method yields a range of wave solutions with distinct shapes, such as optical soliton, optical elliptic, and optical rational soliton solutions. To ensure the results' physical compatibility, we delineated the 2D and 3D plots using appropriate parametric values. The investigation of achieved soliton solutions will provide effective results across transcontinental distances and related phenomena. The method employed in this study is efficient, talented, and dependable for calculating soliton solutions in nonlinear models. We predict that the results obtained in this study will be significant for applications in optical fibers, plasma physics, the telecommunications industry, engineering, and many more. We construct the given equation plane dynamical system in the bifurcation analysis, and provide all possible phase portraits using the Galilean transformation. The last part of the study examines the modulation instability of the concatenation model. [ABSTRACT FROM AUTHOR]

We theoretically investigate the soliton dynamics of ferroelectric liquid crystal materials used in display devices. The approximations and extensions to existing device technology fields where mathematical analysis would improve optical device development are given special consideration. The ferroelectric liquid crystal maintained between two parallel electrical conductors is taken into consideration in order to illustrate bookshelf geometry. These liquid crystal molecules are influenced by an electric field due to their spontaneous polarization. The effect of electric fields and molecular excitations has been successfully established. We study Hirota's bilinearization method and the (G ′ / G) expansion method for ferroelectric liquid crystals, which can be expressed by the Sine–Gordon equation governing the soliton dynamics in crystal systems. We suggest that this kind of collisional solitonic humps in nematicon profiles indicates the wide range of optical switching strategies for network design and logic gates. This switching mechanism may have enormous applications in multiplexing liquid crystal displays with higher resolution. [ABSTRACT FROM AUTHOR]

The cubic–quartic perturbed Biswas–Milovic equation, which contains Kudryashov's nonlinear form and two generalized nonlocal laws, has been explored qualitatively and quantitatively, as demonstrated in the present work. The research methods used include the complete discrimination system for polynomial method and the trial equation method. The results show that the Hamiltonian has the conservation property, and the global phase diagrams obtained via the bifurcation method reveal the existence of periodic and soliton solutions. Furthermore, we fully classify all the single traveling wave solutions to substantiate our findings, covering singular solutions, solitons, and Jacobian elliptic function solutions. We analyze their topological stabilities and present two‐dimensional graphs of solutions. We also delve deeper into the dynamic system by incorporating the perturbation item to explore the chaotic phenomena associated with the equation. These outcomes are valuable for studying the propagation of high‐order dispersive optical solitons and have potential applications in optimizing optical communication systems to improve efficiency. [ABSTRACT FROM AUTHOR]

Concatenation model assist in optimising the setup for controlling and manipulating the soliton dynamics. Solitons are self-reinforcing solitary waves that maintain their shape and energy over long distances, also have applications in optics and physics. A thorough analysis of the concatenation model, which incorporates a power law nonlinearity, is presented in this work. This investigation also comprises the phenomena of nonlinear chromatic dispersion, which affects optical fibres and other dispersive media that modulates the chromatic dispersion of the material. When nonlinearities like as self-phase modulation and cross-phase modulation are present, the chromatic dispersion coefficient becomes a function of optical intensity. By employing the modified auxiliary mapping scheme, new families of optical dromions (solions) like bright dromion, domain wall, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. are extracted for the suggested model. The two classes of M-shaped analytical rational solutions are also acquired and by selecting the appropriate values for the relevant parameters, their dynamics are visualised in figures. Likewise two different kinds of interactions between M-shaped rational solutions and kink waves are also computed. In addition, we evaluate periodic cross-rational solutions, kink cross-rational solutions, homoclinic breather solutions and multiwaves solutions for the governing model. The derived solutions have confirmed the potency and stability of the current techniques. In addition, certain solutions graphs are also provided to show the physical nature of the derived results. [ABSTRACT FROM AUTHOR]

In this study, we investigate the Biswas–Arshed (BA) model, applicable in various fields such as fluid mechanics, laser science, and nonlinear optics. We employ the direct algebraic procedure, the modified rational sine–cosine process, and the 1 G ′ approach to obtain soliton dynamics of the mentioned model. Chaotic behavior and sensitivity analysis of the BA model are also investigated using a planar dynamic system. As a result, periodic, quasi-periodic, and chaotic patterns are obtained from the suggested nonlinear model. We also obtain various soliton solutions from this model with novel properties. From the proposed equation, we can obtain periodic waves with bright solitons, bright-dark solitons, dark solitons, breather waves with singularities, double periodic waves, periodic waves with singularities, bright solitons with singularities, multiple bright dark breather waves with singularities, and multiple bright breather waves with singularities. Certain features of the outcomes are exhibited in 2D, 3D, and density views. The work presented is innovative as it offers valuable insights into the governing model's intricate behaviors and diverse waveforms through extensive analysis. This study also contributes to understanding real-world problems by incorporating waveform properties, bifurcation analysis, chaotic dynamics, and sensitivity tests. [ABSTRACT FROM AUTHOR]

The nonlinear dispersive eighth-order Schrödinger equation is a mathematical equation that describes the behaviour of complex wave phenomena in specific physical systems. It is utilised in the fields of nonlinear optics and wave propagation. This article examines the eighth-order dispersive nonlinear Schrödinger equation, using the sine-cosine approach to extract optical solitons expressed as sine and cosine functions. The sine-cosine method gives a systematic and efficient strategy for obtaining solitary wave solutions without requiring extensive computational resources. By expanding the solution in terms of sine and cosine functions, the technique transforms the problem into solving a system of algebraic equations, which is often more computationally tractable than other methods. Then solving the obtained algebraic system, the desired solutions are archived. The solutions obtained are then simulated using Mathematica. The results demonstrate bright, bell-shaped and periodic optical solitons for specific parameter values. The obtained results are depicted via 3D and 2D graphs. [ABSTRACT FROM AUTHOR]

In this article, the modified extended Fan sub-equation approach as an analytical tool to investigate the optical soliton solutions of the paraxial wave dynamical model with Kerr media. Indistinguishable and non-diffractive spatially scattered waves transmitting in the optical Kerr medium are explained by optical solitary waves. The solitons, single and mixed non-degenerate Jacobi elliptic function type solutions of the time-dependent dimensionless paraxial wave equation are assembled using the modified extended Fan sub-equation approach. The aforementioned approach offers new, comprehensive solutions that are relatively easy to implement, in contrast to earlier continuous strategies. This technique uses a traveling wave transformation to convert a non-linear partial differential equation into an ODE. The developed wave solutions have substantial significance in the fields of science and engineering. Visual illustrations of various soliton layouts can be achieved by supplying suitable values for the parameters via this technique. The computer software Mathematica 13.2 is used to illustrate several modulus, real, and imaginary solutions visually in the form of contour, 2D, and 3D visualizations that help understand the concrete importance of the paraxial wave dynamical model. The results are fascinating and can potentially be helpful in investigating the stochastic aspects of many nonlinear physical theories that arise in optical studies and a number of other scientific fields. [ABSTRACT FROM AUTHOR]

In this study, we acquired some optical solitons of (3 + 1) dimensional nonlinear Schrödinger equation (3DNLSE) and coupled nonlinear Helmholtz equations (CNLHE) by using generalized G ′ G -expansion method (GEM). We are able to derive exponential, trigonometric, and hyperbolic solutions. We notice that Mathematica 11.2 offer the equations for these answers. Aside from that, we display some of the solution's graphic performance. Recently, accurate traveling-wave solutions for nonlinear partial differential equations (NLPDEs) have been acquired using this technique. Through linear stability analysis, we derive an analytical expression for the instability gain and analyze its main characteristics. Finally, we assess the robustness and stability of the solitary waves through numerical simulations and compare the accuracy of the analytical and numerical results. The obtained ultra-short optical solitons can be widely used as a guide for practical applications in telecommunications domain. [ABSTRACT FROM AUTHOR]

Analytical solutions of the generalized nonlinear Schrödinger with four powers of nonlinearity for description of propagating pulses in optical fiber are presented. Optical solitons corresponding to the mathematical model are given. Conservation laws of the generalized model for propagation pulses with four powers of nonlinearity are written. To the best of our knowledge, the conservation laws obtained have not yet been presented in literature. The equation investigated generalizes several well-known models, which allows us to evaluate the influence of various processes on pulse propagation. Conservative quantities for the bright optical soliton, corresponding to its power, momentum and energy, are calculated. The analytical expressions for conservative quantities obtained can be applied to check whether numerical schemes for the explored equation are conservative. [ABSTRACT FROM AUTHOR]

This paper discusses the time-fractional nonlinear Schrödinger model with optical soliton solutions. We employ the f + ( G ′ G) -expansion method to attain the optical solution solutions. An important tool for explaining the particular explosion of brief pulses in optical fibers is the nonlinear Schrödinger model. It can also be utilized in a telecommunications system. The suggested method yields trigonometric solutions such as dark, bright, kink, and anti-kink-type optical soliton solutions. Mathematica 11 software creates 2D and 3D graphs for many physically important parameters. The computational method is effective and generally appropriate for solving analytical problems related to complicated nonlinear issues that have emerged in the recent history of nonlinear optics and mathematical physics. Furthermore, we venture into uncharted territory by subjecting our model to chaotic and sensitivity analysis, shedding light on its robustness and responsiveness to perturbations. The proposed technique is being applied to this model for the first time. [ABSTRACT FROM AUTHOR]

The new extended direct algebraic technique (EDAT) is used to investigate the rational, and soliton solution for time dependent dimension-less paraxial wave model. The wave solutions help in considerations of physical phenomena and have significant applications in engineering and physics. In optics and photonics, various optical patterns of waves can be beneficial for demonstrating the dynamics behavior of optical solutions that pertain to studying a several kind of mechanical techniques involving the flow of light via optical fibers like mirror, lenses and imaging. By applying suitable parameter values, the exact solutions are obtained with dark, bright, singular, bright-dark, periodic form by using Mathematica 11.0. The 3-D density, 2-D plot and contour plot are plotted and explored the self-focusing structure of electromagnetic waves in non-linear techniques to present a physical description of examined solutions using Matlab. The obtain soliton solutions demonstrate the non-dispersive and non-diffractive localized propagation wave packets in optical kerr media. [ABSTRACT FROM AUTHOR]

The recently reported compactified hyperboloidal method has found wide use in the numerical computation of quasinormal modes, with implications for fields as diverse as gravitational physics and optics. We extend this intrinsically relativistic method into the non-relativistic domain, demonstrating its use to calculate the quasinormal modes of the Schrödinger equation and solve related bound-state problems. We also describe how to further generalize this method, offering a perspective on the importance of non-relativistic quasinormal modes for the programme of black hole spectroscopy.

Optical solitons classically are stationary solutions of the nonlinear Schrödinger equation. We perform a quantum field theoretic treatment by quantising a linearised fluctuation field around the classical soliton solution which can be seen as providing a background spacetime for the field. The linearised fluctuation modifies the soliton background, which is often neglected, reminiscent of the nondepleted-pump approximation. Going beyond this approximation and by using a number-conserving Bogoliubov approach, we find unstable modes that grow as the soliton propagates. Eventually, these unstable modes induce a considerable (backreaction) effect in the soliton. We calculate the backreaction in the classical field fully analytically in the leading second order. The result is a quadratic local decrease of the soliton photon number in propagation due to the backreaction effect of the unstable mode. Provided the initial pulse is close to the classical soliton solution, the unstable mode contributions always become dominant. We also consider practical scenarios for observing this quantum-induced soliton distortion, in the spectral domain. The backreaction, which we expect to be present in bright and dark, discrete and continuous solitons and other nonlinear pulses plays an important role in future optical analogue gravity experiments, for soliton lasers, and optical communications.

This current research explores a new generalized q-deformed sinh -Gordon equation. The governing equation is frequently used to model plasma-based solutions, complex optical science, photonic transmission systems, ultrashort burst lasers to identify objects and other theoretical sciences. The work consists of two goals. Firstly, analytically using the modified extended tanh function approach. Precise results for the derived equation are obtained that could be used to simulate physical systems with broken symmetries and to consider events involving amplification or dissipation. Secondly, with the help of a numerical approach investigate the error function between the q-demormed terms. Several figures have been included to illustrate the different optical solitons propagation patterns. [ABSTRACT FROM AUTHOR]

Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission. [ABSTRACT FROM AUTHOR]

This investigation focuses on the construction of novel dark and singular soliton solutions for the Hirota equation, which models the propagation of ultrashort light pulses in optical fibers. Initially, we employ a wave variable transformation to convert the physical model into ordinary differential equations. Utilizing extended rational sinh–cosh and sine–cosine techniques, we derive an abundant soliton solution for the transformed system. By plugging these explicit solutions back into the wave transformation, we obtain dark and singular soliton solutions for the Hirota equation. The dynamic evolution of dark soliton profiles is then demonstrated, with a focus on varying physically significant parameters such as wave frequency, strength of third-order dispersion, and wave number. Furthermore, a comprehensive analysis is examined to elucidate how the dark and singular soliton profiles undergo deformation in the background influenced by these arbitrary parameters. The findings presented in this study offer valuable insights that could potentially guide experimental manipulation of dark solitons in optical fibers. [ABSTRACT FROM AUTHOR]

The Sasa-Satsuma (SS) equation is studied in this research study using ideas from planar dynamical theory and the beta differential operator. The SS equation is converted into two ordinary differential equations by applying the Galilean transformation. The work is since concentrated on examining the system's bifurcation points and equilibrium points. The sensitivity of the linked system to its initial values is demonstrated via graphical representations. In order to examine chaos and phase transitions, the system is changed by adding the periodic function cos (ω t) . This modification is done as part of this study. Specific optical soliton solutions are illustrated using the first integral technique. Additionally, for various combinations of frequency and amplitude values, numerical simulations are demonstrated the existence of unusual chaotic attractors, such as candy-type, torus-type, and multiscroll chaotic structures. The impact of the beta differential operator on the amplitude of various optical solitons, such as bright, dark, W-shaped, and breather solitons, are also studied. [ABSTRACT FROM AUTHOR]

In this paper, we present an innovative approach to acquire the exact solutions of the Shynaray-IIA equations (S-IIAE), by using the improved modified Sardar sub-equation method (IMSSEM). The S-IIAE are nonlinear and coupled partial differential equations that arise in various fields of physics and engineering such as optical fibers and ferromagnetic materials. The IMSSEM is applied to S-IIAE; we successfully derived exact solutions that accurately described the wave propagation behavior of the system under consideration. The obtained solutions include rational, trigonometric, and trigonometric hyperbolic function solutions. The obtained solutions are concise and offer a deeper insight into the dynamics and characteristics of the S-IIAE. Moreover, some of the new solutions to S-IIAE are plotted in different dimensions through which bright, anti-kink and bright solitary wave structures are established. The results of the study also indicated that the proposed method is a valuable approach for achieving analytical solutions to a wide range of nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

This manuscript presents some new exact solutions for the dispersive Schrödinger Hirota's (SH) equation considering the effects of spatio-temporal dispersion with parabolic law nonlinearity. A wave transformation technique is implemented to transform the SH equation into a nonlinear ordinary differential equation. The solutions for the dispersive SH equation are derived using the modified extended tanh approach. These solutions exhibits various sorts of solitons, including bright, dark, periodic, and singular solitons. The findings of this research hold potential significance in the domain of fiber-optic communication, as they contribute to a deeper understanding of soliton dynamics. [ABSTRACT FROM AUTHOR]

Because it is used in communication and information technology, the propagation of pulses in optical fibers has become a significant research subject in recent years. Mathematical models have been created to describe the behaviors of optical solitons in optical fibres, such as the Kaup-Newell equation, the nonlinear Schrödinger equation with various types of nonlinearity, and others. A model among these is the newly generalized nonlinear Schrödinger equation with triple refractive index and non-local nonlinearity. To secure optical solitons for a particular case of this novel model, we used the improved modified extended tanh function approach. Different solutions have been acquired such as bright solitons, dark solitons, singular solitons, singular periodic solutions, trigonometric solutions, and hyperbolic solutions. Some of the discovered solutions are shown in 2D and 3D graphs for better comprehension and demonstration.

This study thoroughly analyzes the concatenated model in the field of optical communication. The chaotic behavior of the system is examined using a periodically perturbed system, which incorporates time series analysis, Poincaré sections, and bifurcation diagrams. The study constructs periodic solutions, solitary wave solutions, and kink wave solutions by integrating along the level curves of the Hamiltonian system. Additionally, singular periodic solutions and Jacobian elliptic functions are derived to gain further insight into the dynamics of the model. The significance of this study is emphasized through a comparative analysis with existing literature, highlighting the novelty of the findings in understanding the dynamics of concatenated models. The result has theoretical and practical significance for deepening the study of wave propagation in the field of optical communication.

In this paper, the modified extended direct algebraic technique is used for determining new and various traveling wave solutions to the coupled nonlinear Schrödinger equation (NLSE) with Kudryashov's law of nonlinearity. This model describes the propagation of optical solitons through magneto-optic wave-guides. Various solutions such as dark solitons, singular solitons, hyperbolic solutions, singular periodic solutions, rational solutions, Jacobi elliptic solutions and Weierstrass elliptic function solution are raised. To demonstrate the physical behavior of the obtained solutions, 3D and 2D graphs are introduced.

This study investigates the (1+1) dimensional dissipative nonlinear Schrödinger equation, which has applications in modeling the evolution of swell in the ocean. Two different and impressive techniques are used for the solutions, which are the Jacobi elliptic function expansion method and the sine-Gorgon expansion method. The suggested techniques are designed to derive the solutions for many other the nonlinear partial differential equations that arising in various branches of sciences. By applying this methods, we obtain novel soliton solutions, which are expressed in terms dark, bright, singular and combo optical solitons. The efficient optical soliton solutions discovered through this methods have the potential to find use in a variety of fields, inclusive electronics, ocean waves, and optical fibers. The modulation instability criterion for governing model is obtained based on the standard linear stability analysis. Additionally, we will also present graphs in 2D and 3D form with constraints conditions. [ABSTRACT FROM AUTHOR]

The stationary solution and the dynamical evolution of the fundamental and higher eigenmodes of the parity-time ( $ \mathcal {PT} $ PT ) symmetric coupled system with self-defocusing Kerr nonlinearity have been analysed. The eigenstates of the high and low-frequency modes and the threshold condition for the $ \mathcal {PT} $ PT -symmetric phase transition have been discussed. The propagation dynamics and stability of the stationary solutions have also been analysed. The eigenmodes are linearly stable and propagate with constant power in the $ \mathcal {PT} $ PT -symmetric regime. The study has been extended to analyse the variation of the power using the semi-analytical approach. Nonlinear $ \mathcal {PT} $ PT -symmetric coupled systems with balanced gain/loss give rise to interesting physical phenomena and have applications in various fields like all-optical signal manipulation. [ABSTRACT FROM AUTHOR]