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This template retrieves M-shaped rational solitons and their interactions with kink waves, homoclinic breathers, multiwave, Grey-black optical solitons, periodic cross-rational solitons and kink cross-rational solitons propagation in optical fibers where self-phase modulation (SPM) is negligibly minor and therefore removed. The proposed equation contains spatio-temporal dispersions (STD), of second and third orders, to recompense for small group velocity dispersion (GVD). All new analytical solutions are found by utilizing the symbolic computation with logarithmic transformation and ansatz functions approach. Moreover, stability characteristics of all solutions are found. [ABSTRACT FROM AUTHOR]

The current paper reveals optical soliton solutions to the concatenation model in birefringent fibers. Two integration approaches are adopted in the paper. They are the enhanced Kudryashov approach and the new projective Riccati equation's method. These reveal soliton and complexiton solutions that the method of undetermined coefficients failed to recover in earlier work. The parameter constraints are also displayed for the existence of the solitons and complexitons. [ABSTRACT FROM AUTHOR]

A full spectrum of optical gap solitons in fiber Bragg gratings with cubic-quartic dispersive reflectivity is identified. The nonlinear refractive index structure is of parabolic law type. When the modulus of ellipticity approaches unity, the limiting approach to the retrieved Jacobi's elliptic functions reveals the soliton solutions. [ABSTRACT FROM AUTHOR]

This paper uses the classical Lie symmetry method for optical solitons to study the Chen-Lee-Liu equation. We are able to establish symmetries that convert the model into a set of ordinary differential equations and obtain solutions of the reduced equations through various methods. [ABSTRACT FROM AUTHOR]

The fractional Lakshmanan–Porsezian–Daniel equation (LPD) is a significant complex model for the fractional Schrödinger family which arises in quantum physics. This paper explores new bright and kink soliton solutions of the space-time fractional LPD equation with the Kerr law of nonlinearity. By considering the conformable derivatives, the governing model is translated into integer-order differential equations with the aid of an appropriate complex traveling wave transformation. Dynamic behavior and phase portrait of traveling wave solutions are investigated. Further, various types of bright and kinked soliton solutions under definite parametric settings are discussed. Moreover, graphical representations of the obtained solution of the diverse fractional order are depicted to naturally illustrate the constructed solution. [ABSTRACT FROM AUTHOR]

The principal purpose of this research is to utilize the exp-function approach for achieving exact solutions of nonlinear optical fibers, including fractional order in the sense of conformable derivatives. Owing to the algorithm of symbolic computational, Some soliton solutions are obtained, including solitary soliton, singular kink-type soliton, and periodic solitons. These results are generated and developed by using the exp-function. To the greatest of our knowledge, the soliton solutions given in this study could be highly beneficial in comprehending physical phenomena. [ABSTRACT FROM AUTHOR]

The paper aims to construct optical solitons and travelling wave solutions to two birefringent nonlinear models which consist of two-component form of vector solitons in optical fibre: the Biswas–Arshed model with Kerr-type nonlinearity and without four-wave mixing terms and the nonlinear Schrödinger equation with quadratic-cubic law of refractive index along with four-wave mixing terms. These nonlinear Schrödinger equations are applied in many physical and engineering fields. Optical solitons are considered in the context of photonic crystal fibres, couplers, polarisation-preserving fibres, metamaterials, birefringent fibres, and so on. Two reliable integration architectures, namely, the extended simplest equation method and the generalised sub-ODE approach, are adopted. As a result, bright soliton, kink and dark soliton, singular soliton, hyperbolic wave, a periodic wave, elliptic function solutions of Weierstrass and Jacobian types, and other travelling wave solutions, such as breather solutions and optical rogons, are derived, together with the existence conditions. In addition, the amplitude and intensity diagrams are portrayed by taking appropriate values for a few selected solutions. Furthermore, based on linear stability analysis, the modulation instability was explored for the obtained steady-state solutions. The reported results of this paper can enrich the dynamical behaviours of the two considered nonlinear models and can be useful in many scientific fields, such as mathematical physics, mathematical biology, telecommunications, engineering and optical fibres. This study confirms that the proposed approaches are sufficiently effective in extracting a variety of analytical solutions to other nonlinear models in both engineering and science. [ABSTRACT FROM AUTHOR]

Softphotonics has emerged as a new discipline that utilizes soft matter (i.e., liquids, gels, bio‐materials) as waveguide materials with versatile functionalities. The flexible properties of soft matter show great potential for further exploiting nonlinear in‐fiber phenomena to gain more insights into their fundamental dynamics and to inspire a new generation of broadband optical light sources and signal processors that are adaptable, reconfigurable, and biocompatible. In particular, incorporating solvents with extraordinary temperature sensitivity, miscibility, and nonlinearity into optical fibers has spawned a series of inventions and fundamental scientific findings over the last decades. This review highlights the current state of development of nonlinear photonics in liquid‐filled fibers. The current state of knowledge in the linear and nonlinear material properties of the most prominent solvents (CS2, CCl4, C2Cl4, benzene and its derivatives) are revisited, and recent advances in nonlinear liquid‐core fiber optics, including a special highlight on phenomena that are unique to liquids, such as modified solitary states and local dispersion control are summarized. Finally, the leading scientific challenges for advancing the field, which highlights liquid‐core fibers as a rich platform for science and technology, are discussed. [ABSTRACT FROM AUTHOR]

Coupling between modes is crucial for generating coherent structures and spatiotemporal chaos in optical systems. In an ultrafast fiber laser with birefringence, the stable pulse is viewed as a vector soliton (VS) with two orthogonal modes nonlinearly coupled through the Kerr effect and gain/loss. However, the dynamics of a VS in the presence of linear coupling is unperceived despite linear coupling playing a significant role in various optical systems. Here, it is shown that a local linear coupling between polarization modes in lasers facilitates brand‐new nonlinear states, including stationary, breathing, and chaotic VSs. The observed solitary states can be regarded as emergent phenomena when two particles (polarization modes) in a system have a simple interaction (linear coupling), which are ubiquitous in biology, chemistry, and complex systems. It is found that linear coupling is essential for sustaining the internal balance between two modes within the VS. Chaotic dynamics of VS emerge under weak linear coupling, while the two modes lose trapping due to the birefringence in the absence of linear coupling. This work can offer new insight into the two‐mode nonlinear system and inspire research interests in the intelligent manipulation of ultrashort pulse lasers. [ABSTRACT FROM AUTHOR]

In this paper, the improved nonlinear Schrödinger equation with dual-power law nonlinearity and Hamiltonian perturbation terms describing the dynamics of ultrashort pulse propagation in nano optical fibers is researched. Numerous exact solutions and corresponding nonlinear chirps of this equation are received by using the complete discrimination system for polynomial method and direct integral method. And several emblematic two-dimensional graphs are drawn under specific parameters, which can identify the morphology of optical waves more intuitively. [ABSTRACT FROM AUTHOR]

We report the generation of multimode solitons in step-index fibers. The solitons are superpositions of 5–10 temporally aligned transverse modes, they exhibit speckled beam profiles, and the spatio-spectral variation across the soliton can be complex. A greater understanding of multimode solitons should create a foundation for further research into complex multimode nonlinear phenomena in step-index fibers. With energies of tens of nanojoules and durations around 100 fs, the multimode solitons are speckled fields with peak powers that can exceed 300 kW, parameters that may be valuable in applications. [ABSTRACT FROM AUTHOR]

In many nonlinear partial differential equations, noise or random fluctuation is an inherent part of the system being modeled and have vast applications in different areas of engineering and sciences. This objective of this paper is to construct stochastic solitons of Biswas-Arshed equation (BAE) under the influence of multiplicative white noise in the terms of the Ito calculus. Bright, singular, dark, periodic, singular and combined singular-dark stochastic solitons are attained by using the Sardar subequation method. The results prove that the suggested approach is a very straightforward, concise and dynamic addition in literature. By using Mathematica 11, some 3D and 2D plots are illustrated to check the influence of multiplicative noise on solutions. The presence of multiplicative noise leads the fluctuations and have significant effects on the long-term behavior of the system. So, it is observed that multiplicative noise stabilizes the solutions of BAE around zero. [ABSTRACT FROM AUTHOR]

In physics, mathematics, and other disciplines, new integrable equations have been found using the P-test. Novel insights and discoveries in several domains have resulted from this. Whether a solution is oscillatory, decaying, or expanding exponentially can be observed by using the AEM approach. In this work, we examined the integrability of the triple nonlinear fractional Schrödinger equation (TNFSE) via the Painlevé test (P-test) and a number of optical solitary wave solutions such as bright dromions (solitons), hyperbolic, singular, periodic, domain wall, doubly periodic, trigonometric, dark singular, plane-wave solution, combined optical solitons, rational solutions, etc., via the auxiliary equation mapping (AEM) technique. In mathematical physics and in engineering sciences, this equation plays a very important role. Moreover, the graphical representation (3D, 2D, and contour) of the obtained optical solitary-wave solutions will facilitate the understanding of the physical phenomenon of this system. The computational work and conclusions indicate that the suggested approaches are efficient and productive. [ABSTRACT FROM AUTHOR]

The fractional-stochastic Fokas-Lenells equation (FSFLE) in the Stratonovich sense is taken into account here. The modified mapping method is used to generate new trigonometric, hyperbolic, elliptic and rational stochastic fractional solutions. Because the Fokas-Lenells equation has many implementations in telecommunication modes, complex system theory, quantum field theory, and quantum mechanics, the obtained solutions can be employed to describe a wide range of exciting physical phenomena. We plot several 2D and 3D diagrams to demonstrate how multiplicative noise and fractional derivatives affect the analytical solutions of the FSFLE. Also, we show how multiplicative noise at zero stabilizes FSFLE solutions.

This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank–Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution.

A four-hole tellurite microstructured optical fiber (MOF) was designed and fabricated based on TeO2–Bi2O3–ZnO–Na2O (TBZN), and the fiber loss was 0.1 dB/m@1550 nm. Based on a 3 m tellurite MOF, dispersive wave (DW) generation and evolution was experimentally investigated at the pump wavelengths of 1778 nm, 1812 nm, and 1878 nm. With the increase of the average pump power, DWs trapped by optical solitons were observed at the blue edge wavelength, but their formation became more and more difficult with the pump wavelength shifting far away from the zero-dispersion wavelength. The variation pattern of center wavelengths and peak powers of the fundamental optical solitons and DWs were investigated: the center wavelength distribution satisfied the group velocity matching; the peak power of the fundamental DW gradually exceeded that of the fundamental optical soliton with the increase of the average pump power. Furthermore, using the generalized nonlinear Schrödinger equation, simulation on the generation of DWs and optical solitons was carried out at 1778 nm, 40 mW, the result of which agreed well with the experimental observation. This investigation is instructive for DW applications in tunable laser sources, wavelength conversion, and time frequency metrology. [ABSTRACT FROM AUTHOR]

This study introduces an analysis of bifurcations, chaotic dynamics, and sensitivity using the Galilean transformation applied to the perturbed non-linear Schrödinger equation (NLSE) with Kerr-law nonlinearity. Additionally, we employ the efficient Sardar sub-equation (Sse) method to derive various optical soliton solutions. Initially, we outline the general framework of the Sse method proposed. Next, we utilize a traveling wave transform on the NLSE, transforming it into a system of nonlinear ordinary differential equations (NLODEs) which are further separated into their real and imaginary components. Furthermore, we apply this method to derive new optical solitons for the NLSE equation with Kerr law. We perform exact analytical simulations of these optical soliton solutions and investigate the effects of different parameters on the soliton waves.

New exact solutions for the perturbation higher order nonlinear Schrödinger equation (NLSE) with dual-power law nonlinearity are investigated using the ϕ6 expansion method. This type of NLSE models the propagation of femtosecond pulses in fiber optics which has many applications such as infrared time-resolved spectroscopy, ultrahigh-bit-rate optical communication systems and ultrafast optics. The application of ϕ6 expansion technique provided many different types of solutions. Dark solitons, bright solitons, singular solitons, hyperbolic solutions, periodic and singular periodic solutions are obtained. The graphical representations of some selected solutions are provided to present both the dynamical behavior of solutions and the effect of changing the nonlinearity degree on their dynamical behavior. This study concludes that the nonlinearity degree controls the dynamical behavior of the light pulse.

The Lakshmanan-Porsezian-Daniel (LPD) model, an extended version of the nonlinear Schrödinger equation, plays a crucial role in comprehending optical solitons—self-reinforcing waves that maintain their form while traveling through a medium. This study employed the G′G2-expansion method to explore the model and present new exact solitary wave solutions with various nonlinearities, including the Kerr, anti-cubic, and parabolic laws. The findings provide solutions for different types of optical solitons, such as bright solitons, dark solitons, rational functions, and periodic solitons. The obtained results offer fresh insights into the complex LPD model, deepening our core understanding of optical soliton dynamics. Importantly, these findings have significant implications for soliton-based applications, specifically in modern communication networks and nonlinear optics, directly impacting optical fiber transmission. Furthermore, the research introduces singular solitons, a unique and highly localized wave phenomenon, through an influential and systematic approach to exact optical solutions for various models. As communication technology and nonlinear optics continue to advance, these findings hold substantial promise for practical applications in the development of cutting-edge optical devices and systems.

The analytical soliton solutions place a lot of value on birefringent fibres. The major goal of this study is to generate novel forms of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which depicts unstable optical solitons that arise from optical propagations using birefringent fibres. The (presumably new) extended direct algebraic (EDA) technique is used here to extract a large number of solutions for RKLE. It gives soliton solutions up to thirty-seven, which essentially correspond to all soliton families. This method's ability to determine many sorts of solutions through a single process is one of its key advantages. Additionally, it is simple to infer that the technique employed in this study is really straightforward yet one of the quite effective approaches to solving nonlinear partial differential equations so, this novel extended direct algebraic (EDA) technique may be regarded as a comprehensive procedure. The resulting solutions are found to be hyperbolic, periodic, trigonometric, bright and dark, combined bright-dark, and W-shaped soliton, and these solutions are visually represented by means of 2D, 3D, and density plots. The present study can be extended to investigate several other nonlinear systems to understand the physical insights of the optical propagations through birefringent fibre.

In this article, the topological phase portrait and dynamical behavior of the coupled Biswas–Arshed equation in single mode polarization-preserving birefringence fibers are discussed via qualitative analysis of planar dynamic system. When assigning values to the parameters of the system with perturbation terms, the system exhibits chaotic behavior. By the polynomial complete discrimination method, the optical solitons are obtained such as dark solitons, bright solitons, dark-bright solitons, and bright-dark solitons. Moreover, the physical properties of optical solitons are studied through two-dimensional and three-dimensional diagrams, density maps and contour maps of optical solitons. Finally, the modulation instability of the system is analyzed via standard linear stability.

The stochastic Sasa–Satsuma equation (SSSE) in the Stratonovich sense is considered here. To produce new elliptic, rational, hyperbolic, and trigonometric stochastic solutions, the modified mapping approach is applied. Due to the fact that the Sasa–Satsuma equation is utilized to explain the propagation of femtosecond pulses in optical fibers, the acquired solutions can be used to describe a wide variety of important physical phenomena. To show how multiplicative noise impacts the analytical solutions of the SSSE, we present a variety of 2D and 3D graphs. We show the stabilization of SSSE solutions by multiplicative noise at zero.

This context focuses on examining the manner in which localized waves travel through a non-linear medium that adheres to a dual-power law. This medium encompasses a range of disruptions like inter modal dispersion, self frequency shift, and self-steepening effects. This investigation entails employing an improved modified extended tanh function (IMETF) technique to obtain various novel optical soliton solutions which include bright, dark, singular and combo singular-dark solitons. Furthermore, we extract singular periodic, exponential, rational, and Weierstrass elliptic solutions. To showcase their physical characteristics, we provide graphical representations in 3D and 2D of some of the derived solutions.

In this paper, we take into account the coupled stochastic Korteweg–De Vries (CSKdV) equations in the Itô sense. Using the mapping method, new trigonometric, rational, hyperbolic, and elliptic stochastic solutions are obtained. These obtained solutions can be applied to the analysis of a wide variety of crucial physical phenomena because the coupled KdV equations have important applications in various fields of physics and engineering. Also, it is used in the design of optical fiber communication systems, which transmit information using soliton-like waves. The dynamic performance of the various obtained solutions are depicted using 3D and 2D curves in order to interpret the effects of multiplicative noise. We conclude that multiplicative noise influences the behavior of the solutions of CSKdV equations and stabilizes them. [ABSTRACT FROM AUTHOR]

The current research analyses several new optical solitons solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with the Kerr law of nonlinearity which arises from the application of the Heisenberg spin chain and fiber optics, via two modified analytical methodologies. The auxiliary equation method (AE) and improved F-expansion method are used to derive several accurate solitary wave solutions of the LPD model. The key objectives of the study are in two folds. Firstly, the implementation of these schemes yields dark, bright, multi-wave, singular, alphabetic and exotic solitons solutions to the model. Secondly, we discuss the stability analysis of our selected model which confirms that the governing model is stable. For understanding the physical configuration of some constructed solitons, we plotted 2D, 3D, contours and density graphs. These solutions secured in this study will play a vital role to understand the exact dynamics of nonlinear phenomena in nonlinear optics and also enhance the previously established results. In the present era of communications network technology and nonlinear optics, the employed techniques seem to be a more categorical, influential and proficient approaches for securing optical solutions to several diversified contemporary models. [ABSTRACT FROM AUTHOR]

This study establishes dispersive solitons of the Schrödinger–Hirota equation in polarization-preserving fibres. The Schrödinger–Hirota equation that governs is examined using the P 6 -model expansion method. Hence, a broad range Jacobi-elliptic solutions, dark, bright, combined dark–bright, singular soliton and periodic wave solutions are produced. [ABSTRACT FROM AUTHOR]

In this manuscript, stationary optical patterns of nonlinear Schrödinger equation for the cubic-quartic form of the refractive index and nonlinear chromatic dispersion are extracted. To investigate exact solutions of the model under observation, unified approach is used. The methodology used is successful for identifying precise outcomes. This analytical approach yields solutions as polynomial and rational functions. Dark and periodic stationary solitons are extracted by choosing the suitable values for the parameters. The model is transformed into a planner dynamical system via the Galilean transformation, and the behavior of bifurcation is documented. By considering every scenario for the parameters, the phase portraits are shown. The obtained results are innovative and they demonstrate the effectiveness and viability of the recommended approaches for analyzing the soliton solutions and phase portraits of diverse nonlinear models. [ABSTRACT FROM AUTHOR]

In this paper, the extended (3+1)-dimensional cubic Schrödinger equation (3D-CNLSE) describes the propagation of pulses in highly nonlinear optical systems solved by the generalized Jacobi elliptic function expansion method. Many novel periodic, hyperbolic, and trigonometric function wave solutions are obtained. The obtained solutions recover some other solutions obtained in the literature and add other new solutions for it. Moreover, the resulting solitary wave solutions can take many different shapes like periodic, kink soliton, and bright solitons. To illustrate the dynamics of the different solitary wave solutions we have chosen to plot the periodic and the kink wave solutions in a medium with self-focusing Kerr-nonlinearity and the bright soliton wave in a medium with self-defocusing nonlinearity every wave was drowned in the 3D, Density, and 2D and it was clear that the solitary wave shape is affected by the choices of the parameters represented the medium. [ABSTRACT FROM AUTHOR]

The generalised Schrödinger equation is a nonlinear equation that is frequently encountered in modern physics study. Additionally, it is an important equation for researching problems with light pulse transmission in nonlinear dispersive optical medium. Schrödinger–Hirota model is very important in communication systems because its refer to motion of solitary wave in optical fiber. In the ongoing study, the modified extended direct algebraic integration technique is applied to study the generalized Schrödinger–Hirota equation. Based on this method, various types of solutions, such as bright solitons, dark solitons, singular solitons, singular periodic solutions, exponential solutions, Weierstrass elliptic solutions and complexiton solutions are extracted. The extracted solutions confirmed the efficacy and strength of the current technique. To illustrate the physical characteristics of the established solutions, many selected solutions are visually depicted. [ABSTRACT FROM AUTHOR]

In this work, we investigate diverse analytical solutions and modulation instability of the nonlinear Schrödinger equation with an anti-cubic nonlinear term. We use the traveling wave transformation and the New Generalized Extended Direct Algebraic Method to perform a variety of exact traveling wave soliton-like solutions. The obtained solutions are among other trigonometric function solutions, complex soliton solutions, and rational solutions. A particular behavior has been depicted in self-focusing and defocusing nonlinearity where dark soliton changes to super rogue waves and breather soliton is obtained. We then use the linearizing scheme to get the growth rate of modulation instability. For a specific value of the excitation wave number and a specific time of simulation, diverse waveforms of the modulated waves are obtained. We have demonstrated that the combined dispersion and nonlinear terms, as well as the anti-cubic nonlinear term, can develop modulation instability. To confirm the predictions based on the analytical results, we use the direct numerical simulation, from which we have displayed a modulation wave of the growth rate modulation instability. It results equally that the anti-cubic nonlinearity is an important object to control the propagation of the solitonic waves in the nonlinear systems. [ABSTRACT FROM AUTHOR]

A nonlinear Schrödinger equation with the combined effects of variable nonlinearity and generalized external potentials is investigated. Three soliton solutions are generated by means of Darboux method through constructed Lax pair. We attained two constraints related to gain or loss function for considered equation via compatibility condition. Using three soliton solutions, influences of the inhomogeneous nonlinearity and harmonic potential on soliton structures are analysed by properly tailoring the loss or gain parameter. Specifically, via inelastic collision among three solitons, soliton switching characteristics is observed. Additionally, we explore the Modulation instability (MI) through linear stability analysis (LSA) and impact of nonlinearity profile is examined. The trigonometric, exponential and constant values have been chosen for loss or gain parameter to study the effect on the MI gain spectrum. [ABSTRACT FROM AUTHOR]

In this article, we investigate the generalised version of the nonlinear Schrödinger equation namely the fractional Schrödinger–Hirota (NLFSH) equation with third order dispersion and Kerr law of nonlinearity, which describes the dynamics of optical solitons in a dispersive optical fiber. An amelioration of the approaches, namely the improved F-expansion approach and the unified method, are used to formulate the abundant optical solitons. After that, utilizing the aforementioned techniques and computational software, different optical solitons are retrieved, including dark, singular, periodic, rational, hyperbolic solitary wave, and trigonometric function solutions. Secondly, we discuss the stability analysis of our selected model which confirm that the governing model is stable. Additionally, the acquired results demonstrate that the suggested strategies have a significant ability to successfully acquire numerous fresh soliton type solutions for the NLFSH equation. For certain values of the required free parameters, the dynamical behaviours of these solutions are visualised in 2D and 3D using Mathematica 13.0. The acquired findings demonstrate the power, effectiveness, and simplicity of the suggested strategies for finding novel solutions to diverse classes of nonlinear partial differential equations in optical engineering and applied sciences. [ABSTRACT FROM AUTHOR]

This manuscript investigates the cubic–quartic optical solitons in magneto-optical waveguides and other traveling wave solutions to coupled Biswas–Milovic equations with Kudryashov's nonlinear form. The solutions are extracted using the extended F-expansion method. Jacobi elliptical solutions, (bright–dark–singular) soliton solutions, hyperbolic solutions, periodic solutions, rational solutions, and exponential solutions are presented. moreover, a graphical illustration of a few selected results are present to clarify the potency and nature of the raised solutions. [ABSTRACT FROM AUTHOR]

The paper presents the extraction of optical solitons for a nonlinear Schrödinger equation (SE) utilizing the Sine-Cosine expansion technique. Moreover, the model's solitary wave solutions' stability is investigated, and the modulation instability is studied. To understand the behavior of various exact solutions, 3D graphs are created and presented in the paper. The obtained results show the bright optical solitons, optical periodic waves, bell shaped optical solitons and breather type optical solitons for various values of parameters. [ABSTRACT FROM AUTHOR]

In this research, a dynamical (3 + 1)-dimensional nonlinear Schrödinger model (NLSM) is under consideration which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This aforementioned model has been widely applied in Bose–Einstein condensates, nonlinear optical fiber communication plasma physics, hydrodynamics, elastic media and other diversified areas of mathematical physics and engineering. This study has two main objectives. Firstly, to obtain some novel solutions in the shape of singular, dark, periodic and plane wave solutions that are innovative and not previously found in the literature. Secondly, an amended extended tanh-function method with modulation instability (MI) is used for this model. As far as we know, this has never been investigated in this manner. The 2-D, 3-D and contour plots have been defined using the required parametric values to support the results of physical compatibility. According to the examined results, the method used in this study to retrieve consisting and conventional solutions is efficient and more immediate in computing and can be thought of as a useful tool in resolving more difficult problems that arise in the field of engineering, physics, mathematics and fiber optics. [ABSTRACT FROM AUTHOR]

Optical solitons emerging from fiber resonators generally possess similar properties that hinge on the system parameters. However, the generation of wavepackets composed of dissimilar solitons within the same laser cavity is still challenging in ultrafast lasers. Here, we report on heteronuclear multicolor soliton compounds composed of chirp-free conventional solitons and chirped dissipative solitons, by introducing convex-concave frequency phases in mode-locked fiber lasers. In spite of different lasing wavelengths, the dissipative solitons always overlap with the conventional solitons, giving birth to trains of modulated wavepackets. The resonant sidebands of two types of solitons follow from the same phase-matching principle dominated by the absolute value of cavity dispersion. Simulations fully substantiate the experimental results, confirming that the overlapping of two solitons is dominated by the co-action of saturable absorption and group-delay compensation. It is demonstrated that the phase-managed dissipative system is capable of supporting multicolor soliton compounds with distinct properties, offering an effective platform to reveal the interaction of dissimilar nonlinear wavepackets. Optical solitons forming in fiber resonators feature properties that hinge on the system parameters, such as dispersion, nonlinearity, gain, and loss. This work demonstrates the heteronuclear multicolor soliton compounds composed of chirp-free conventional solitons and chirped dissipative solitons, by introducing convex-concave frequency phases in mode-locked fiber lasers. [ABSTRACT FROM AUTHOR]

In this study, generalized higher-order nonlinear Schrödinger equation is under consideration analytically. This equation is used in the field of slowly varying envelope of the electric field in the optical fiber with self-phase modulation, third-order dispersion, self-steepening and stimulated Raman scattering. For the sake of optical solitons and other solutions, we use two methods such as generalized exponential rational function (GERFM) and Sardar subequation method (SSEM). The solutions are gained in different forms such as bright, dark, singular, combo solitons, as well as hyperbolic, trigonometric and rational solutions. Some of the acquired wave solutions are characterized graphically in 3D, contour forms and 2D shapes to illustrate the dynamical behavior. A comparable analysis of this study with the available consequences in literature confirms the innovation and assortment of present accomplished wave solutions and hence enhances the great performance of the employed techniques. The offered method can be utilized to assist complicated models applicable to a wide variety of physical situations. We hope that a wide spectrum of engineering model professionals will find this study to be beneficial. [ABSTRACT FROM AUTHOR]

In this work, we consider a concatenation model that is a concatenated version of the familiar nonlinear Schrödinger's equation, Lakshmanan–Porsezian–Daniel equation and the Sasa–Satsuma equation. With the help of the improved modified extended tanh-function method (IMETFM), new families of solutions are extracted for the proposed model. Bright solitons, dark solitons, combo bright-dark solitons, singular solitons, periodic solutions, exponential solutions, rational solutions and Jacobi elliptic solutions are obtained. The IMETFM enables to recover a wide spectrum of solutions to the governing model. The extracted solutions confirmed the efficacy and strength of the current technique. Moreover, the graphs for some solutions are presented to demonstrate their physical nature. [ABSTRACT FROM AUTHOR]

This article focuses on securing distinct optical solitons to optical fiber with the coupled nonlinear Schrödinger equation. The examined equation is analyzed with the aid of conformable space–time fractional and is known to have a significant role in the propagation of pulses through a two-mode optical fiber and the soliton wavelength division multiplexing. The fractional nonlinear partial differential equations have garnered increased interest since they may be utilized to explain a wide range of complicated physical phenomena and have more dynamic structures of localized wave solutions. New extended direct algebraic method, a relatively recent integration tool, is used to obtain the solutions. The diverse pulses as bright, dark, combo, and singular soliton solutions have been extracted. In addition to aiding in the clarification of fractional nonlinear partial differential equations, the employed method provides previously extracted solutions and extracts new exact solutions. Given the correct parameter values, numerous graph forms are sketched to provide information on the visual presentation of the obtained findings. The achieved solutions are to be attractive to researchers for understanding the complexity of the considered model. The findings of this research validate the effectiveness of the proposed method for increasing nonlinear dynamical behavior. It is anticipated that, the research will be of interest to all engineers who work with engineering models. Results demonstrate the efficacy, simplicity, and generalizability of the selected computational method. [ABSTRACT FROM AUTHOR]

In this investigation, we utilize advanced versions of the Extended Direct Algebraic Method (EDAM), namely the modified EDAM (mEDAM) and r+mEDAM, to explore families of optical soliton solutions in the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model (FPRKLM). Our study stands out due to its in-depth investigation and the identification of multiple localized and stable soliton families, illuminating their complex behavior. We offer visual validation via carefully designed 3D graphics that capture the complex behaviors of these solitons. The implications of our research extend to fiber optics, communication systems, and nonlinear optics, with the potential for driving developments in optical devices and information processing technologies. This study conveys an important contribution to the field of nonlinear optics, paving the way for future advancements and a greater comprehension of optical solitons and their applications. [ABSTRACT FROM AUTHOR]

The stochastic Fokas system (SFS), driven by multiplicative noise in the Itô sense, was investigated in this study. Novel trigonometric, rational, hyperbolic, and elliptic stochastic solutions are found using a modified mapping method. Because the Fokas system is used to explain nonlinear pulse propagation in monomode optical fibers, the solutions provided may be utilized to analyze a broad range of critical physical phenomena. In order to explain the impacts of multiplicative noise, the dynamic performances of the different found solutions are illustrated using 3D and 2D curves. We conclude that multiplicative noise eliminates the symmetry of the solutions of the SFS and stabilizes them. [ABSTRACT FROM AUTHOR]

In the current paper, a full spectrum of 1-soliton solutions to the concatenation model with the power-law of self-phase modulation has been recovered. The method of undetermined coefficients has permitted us to solve this problem successfully. The parameter constraints naturally emerge from the derivation and are also listed, guaranteeing these solitons' existence. It has been proved that dark solitons and singular solitons of a specific type would exist only when the power-law parameter collapses to unity. [ABSTRACT FROM AUTHOR]

This paper retrieves numerically the bright and dark 1-soliton solutions for the newly constructed concatenation model using the Laplace-Adomian decomposition technique. The errors analysis is also conducted, and they are of the order of 10-9. The surface, sectional, and error plots are exhibited for bright and dark solitons. [ABSTRACT FROM AUTHOR]

The current paper focuses on the retrieval of solitons in magneto-optic waveguides for the concatenation model having Kerr law of nonlinear refractive index. The simplest equation approach as well as the extended simplest equation method collectively reveal a full spectrum of soliton solutions to the model. The parameter constraints guarantee the existence of such solitons. [ABSTRACT FROM AUTHOR]