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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]

Mode‐locked fiber lasers are applied in versatile scientific fields and exhibit a rich diversity of nonlinear dynamics. However, the nontrivial coexistence of solitons and embedded dispersive wave radiation prevents unveiling the real nonlinear dynamics in mode‐locked fiber lasers, such as multiple solitons interaction. Here, nonlinear Fourier transform (NFT) is applied as a signal processing tool to reveal nonequilibrium multiple soliton dynamics. It is feasible to isolate solitons from the continuous wave background in a fiber laser. The real‐time coherent homodyne detection methodology is used to measure the full‐field dynamic evolution of multiple solitons, including multiple solitons buildup and sequentially nonequilibrium evolution with complex splitting, drifting, and collision processes. With the approach of inverse NFT, the corresponding various pure solitons buildup and collision are reconstructed. The eigenvalue probability distributions are used to classify different lasing regimes. Moreover, the controllable multiple solitons drifting is achieved and characterized by using all‐optical methods. Experimental results suggest that NFT can be used to identify localized soliton nonequilibrium evolution excluding dispersive wave radiation influence, which provides a new window into the physics of the underlying laser dynamics and uncovers real soliton interaction in dissipative nonlinear systems. [ABSTRACT FROM AUTHOR]

This study attempts to investigate the dynamic study of the three-component coupled NLS-type equations. The unified Riccati equation expansion method and the generalized Kudryashov method are used to construct the optical solitons, including the periodic function solution, the trigonometric function solution, the exponential function solution, the solitary wave solution, and the elliptic function solution. The results of this investigation will contribute in gaining a better understanding of the overall illustration of the soliton dynamics system. For the sake of physical demonstration and visual presentation, we graphically illustrate some of the identified solutions in 3D, density and 2D plots using Mathematica software. Moreover, the sensitivity analysis of the proposed system is performed, and it is observed that the given system is highly sensitive, as a small change in the initial conditions causes an abrupt change in the solutions. These outcomes demonstrate that these three strategies are more efficient, simple, and trustworthy than other nonlinear physical system solving techniques developed in nonlinear sciences. [ABSTRACT FROM AUTHOR]

This paper studies the (1 + 1) -dimensional nonlinear Schrödinger equation via polynomial law of nonlinearity which arises in nonlinear optical fibers and Bragg gratings. The envelope solitons as a entire are separated into two types: dark and bright solitons, which exist in the anomalous and normal dispersion regions, respectively. Grey and black optical solitons of the stated model are reported through appropriate complex envelope ansatz solution. With the usage of Chupin Liu's theorem to the grey and black solitons, we evaluate new categories of combined optical soliton solutions. In addition, propagation behaviours for homoclinic breathers, multiwaves and M-shaped rational solitons are analytically examined via logarithmic transformation with ansatz functions approach. Multiwave solitons are reported by using three-waves technique. Furthermore two kinds of interactions for M-shape soliton through exponential functions are examined. [ABSTRACT FROM AUTHOR]

The main focus of this study is to extract the optical solitons of the two variants of the nonlinear Schrödinger model including the dispersive cubic-quintic nonlinear Schrödinger equation and nonlinear Schrödinger equation with group velocity dispersion. These models have dynamic applications in diversified domains of applied sciences, optical engineering and can be used in the propagation of light in nonlinear optical fibers. For this purpose, a well-organized method called the exp -function method is implemented and derives optical soliton in the shape of dark, bright, periodic and kink. To validate the physical compatibility of the results, the 2D, 3D, contour, and density plots have been outlined using appropriate parametric values which assist the investigators to comprehend the physical phenomena of the governing equation. The results established in this manuscript are fresh and extend the numbers of previously published results. The acquired solutions exhibit that the applied computational methodology used is brief, concise, and reliable, resulting in fewer computations and broad applicability. The scrutinized wave's outcomes are trustworthy to the researchers and also have imperious applications in mathematics and optical physics. [ABSTRACT FROM AUTHOR]

This paper focuses on the use of the Sardar sub-equation method to obtain optical solitons for a nonlinear model that incorporates Kudryashov's quintuple power law and dual-form nonlocal nonlinearity. The model studies the propagation of pulses in optical fibers and the proposed technique is used to investigate various types of solitons including bright, dark, singular, periodic, combined dark-bright, and combined dark-singular solitons. The proposed technique is highly efficient and can also be utilized to solve higher-order nonlinear partial differential equations in fields such as fluid mechanics, plasma physics, and fiber optics. The paper includes a comparative analysis of the model and presents graphical representations for some of the obtained solutions. [ABSTRACT FROM AUTHOR]

In this paper, the functional variable method is used to obtain new optical soliton solutions for the perturbed stochastic nonlinear Schrödinger equation with generalized anti-cubic nonlinearity and multiplicative white noise. Using some transformations, new rational, Jacobi elliptic, Weierstrass, and hyperbolic stochastic solutions are obtained. Several optical soliton solutions were proposed, including dark, bright, and compacton soliton solutions. Graphical presentations of the obtained optical soliton solutions are shown to illustrate some of its physical parameters. [ABSTRACT FROM AUTHOR]

This study presents a novel modification of the Sardar sub-equation method for solving the nonlinear SchrÖdinger equation (NLSE) with second order spatiotemporal dispersion and group velocity dispersion, which is used to describe and model the propagation of optical solitons in nonlinear media. The modification is based on introducing a new function that is used to approximate the solution of the equation. By applying this modified method, we are able to obtain exact analytical solutions for the NLSE with several classes of optical soliton solutions. The method is tested on a variety of nonlinear optical systems and is shown to be highly effective in producing accurate solutions. The results of this study demonstrate the potential of this novel approach for solving the NLSE in the context of optical solitons. These soliton solutions are of great importance in the field of science, physics, mathematics, and engineering. [ABSTRACT FROM AUTHOR]

In this study, the optical solitons of nonlinear Schrödinger equation with anomalous dispersion are investigated via Improved Bernoulli Sub-Equation Function Method (IBSEFM). The obtained solutions are examined by considering their typical behavior in 3D and 2D plots according to the suitable values using software.It is demonstrated that IBSEFM provides a powerful mathematical tool for solving nonlinear models in mathematical physics. [ABSTRACT FROM AUTHOR]

In this study, through the (m + 1 G ′ ) -expansion method, we extract soliton solutions to the coupled-Higgs equation. The studied nonlinear model is known to describe Higgs mechanism. The Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. The proposed method is one of the most powerful methods for constructing soliton solutions for nonlinear partial differential equations. The obtained wave solutions include exponential, hyperbolic, and distinct structures of complex function solutions. The presented results may be helpful in explaining the physical features of various nonlinear physical phenomena. In order to analyze the dynamic behavior of all obtained solutions, we plot three-dimensional and two-dimensional graphs for the obtained solutions. [ABSTRACT FROM AUTHOR]

This paper presents optical solitons with the concatenation model having spatio-temporal and chromatic dispersions. This model can advantageously curtail the Internet bottleneck effect. Two integration schemes yield these solitons. By utilizing the multipliers approach, the conservation laws are also derived. [ABSTRACT FROM AUTHOR]

The article discusses the generation of terahertz optical solitons using dispersion-compensated antenna-coupled planarized ring Quantum Cascade Lasers (QCL). The researchers address the challenges of achieving solitons in terahertz ring QCLs, including dispersion compensation and power extraction. They propose a double waveguide structure and a planarization technique to overcome these challenges.

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. [ABSTRACT FROM AUTHOR]

We investigate deformed/controllable characteristics of solitons in inhomogeneous parity-time (P T) -symmetric optical media. To explore this, we consider a variable-coefficient nonlinear Schrödinger equation involving modulated dispersion, nonlinearity, and tapering effect with P T -symmetric potential, which governs the dynamics of optical pulse/beam propagation in longitudinally inhomogeneous media. By incorporating three physically interesting and recently identified forms of P T -symmetric potentials, namely, rational, Jacobian periodic, and harmonic-Gaussian potentials, we construct explicit soliton solutions through similarity transformation. Importantly, we investigate the manipulation dynamics of such optical solitons due to diverse inhomogeneities in the medium by implementing step-like, periodic, and localized barrier/well-type nonlinearity modulations and revealing the underlying phenomena. Also, we corroborate the analytical results with direct numerical simulations. Our theoretical exploration will provide further impetus in engineering optical solitons and their experimental realization in nonlinear optics and other inhomogeneous physical systems. [ABSTRACT FROM AUTHOR]

This paper seeks to find optical soliton solutions for Lakshmanan–Porsezian–Daniel (LPD) model with the parabolic law of nonlinearity. The spatiotemporal dispersion is included to the model, as it can contribute to handling the problem of internet bottleneck. This study was performed analytically using the traveling wave hypothesis to reduce the model to an integrable form. Then, the resulting equation was handled with two approaches, namely, the auxiliary equation method and the Bernoulli subordinary differential equation (sub-ODE) method. With an intentional focus on hyperbolic function solutions, abundant optical soliton waves including W-shaped, bright, dark, kink-dark, singular, kink, and antikink solitons were derived with the existing conditions. Furthermore, the behaviors of some optical solitons are illustrated. The spatiotemporal dispersion was found to significantly affect the pulse propagation dynamics. Finally, the modulation instability (MI) of the LPD model is explained in detail along with the extraction of the expression of MI gain. [ABSTRACT FROM AUTHOR]

Nematicons became a key topic of interest in liquid crystal technology in recent years. This paper contributes in understanding the fantastic features of nematicons in optics and further disciplines. This piece of research investigates nematicons for obtaining various exact solutions for Kerr and non-Kerr law nonlinearities with the help of the Kudryashov's approach and the tanh–coth technique. The acquired outcomes involve rational, periodic and hyperbolic solutions as well as their combo-type solutions for all the four cases of nonlinearity. A comparative study is conducted to show the novelty of present results with results already existing in the literature. The constraint conditions obtained ensured that the existence of these solutions is extraordinarily favorable to further investigate the dynamics of nematicons for various kinds of nonlinearity. The dynamics of the few of the obtained solutions are also discussed by 3D plots. [ABSTRACT FROM AUTHOR]

This paper explores the new (3 + 1) -dimensional nonlinear Schrödinger equation which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This equation is newly derived based on the extended (3 + 1) -dimensional zero curvature equation. An effective technique, namely, the extended sinh-Gordon equation expansion method is applied to find optical soliton solutions and other solutions for this model. As a result, dark, bright, combined dark–bright, singular, combined singular soliton solutions, and singular periodic wave solutions are obtained. The stability of the model is investigated by using the modulation instability analysis which guarantees that the model is stable and all solutions are stable and exact. Physical explanations of the obtained solutions are presented by using 3D and 2D plots. The reported outcomes are useful in the empirical application of fiber optics. [ABSTRACT FROM AUTHOR]

Nonlinear Schrödinger equation plays a significant role in the description of propagation of light in nonlinear optical fibers. In this manuscript, the nonlinear Schrödinger equation is considered with anti-cubic law of nonlinearity. Chirped optical soliton solutions and chirp-free solutions are extracted for the proposed equation using the generalized projective Riccati equation technique and two variables G ′ G , 1 G -expansion technique. To better comprehend the dynamic characteristics of the retrieved solutions their graphical visualization are provided. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the dynamical behavior of (1 + 1) -dimensional Kudryashov's equation with generalized anti-cubic nonlinearity by extracting the exact closed form solitons and other traveling wave solutions. This nonlinear mathematical model explains the propagation of pulses though optical fibers. It is based on the well-known nonlinear Schrödinger equation with an arbitrary power nonlinearity. In this paper, two techniques are used to extract the optical solitons and other solitary wave solutions of Kudryashov's equation. One is the general projective Riccati equation method and the other is the Jacobi elliptic method. The proposed techniques retrieve the explicit solution expressions by calculating the coefficients of a truncated power series. The exact solutions are obtained in terms of hyperbolic, trigonometric and Jacobi elliptic functions. The constructed solitons include kink, combo dark-bright and dark solitons. Periodic traveling wave solutions are also reported. The derived solutions are shown as three-dimensional graphs for the appropriate choice of parametric parameters. The corresponding two dimensional contour graphs are included to understand dynamical behavior of obtained results. [ABSTRACT FROM AUTHOR]

The φ 6 -model expansion approach is presented to achieve optical soliton solutions for the Fokas-Lenells model. We apply a variable relation to translate the model's partial differential form into an ordinary differential form. Then Maple-18 software applies the abovementioned methods to the governing model. The combination of trigonometric, hyperbolic, and rational function solutions yields various novel dynamical optical solitons. These solutions can all be found with double periodic waves, W-shape periodic waves, and W-shape periodic waves with multiple waves in these solutions. Additionally, local breather waves and multiple bright-dark breather waves are retrieved. Graphical displays of the derived solutions' many dynamic aspects are provided. According to the obtained results from this study, we can say that the adopted technique is effective, relaxing, suitable, and advantageous for solving various nonlinear problems. [ABSTRACT FROM AUTHOR]

In this paper, we studied conformable resonant nonlinear Schrödinger's equation (CRNLSE) incorporating Kerr law nonlinearity. The task is assisted with the help of a couple of robust techniques such as the new extended direct algebraic method and tanh - coth method. The application of these techniques results in a number of novel and interesting solutions such as bright-dark, singular, kink, periodic, and rational solutions alongside their constraint conditions. Moreover, some of the solutions are displayed in 3D and 2D graphs to highlight the physical features of these solutions. The impact of conformable fractional parameters is also studied on the shape dynamics of these solutions through 2D graphs. Proposed solutions show that these methods are effective and powerful for finding traveling wave solutions. [ABSTRACT FROM AUTHOR]

We investigate the bounded travelling wave solutions of the Biswas-Arshed model (BAM) including the low group velocity dispersion and excluding the self-phase modulation. We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media. The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areas which correspond to different phase portraits. All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits. We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity. We present more bounded optical shock waves, the bright-dark solitary wave, and optical rogue waves for the structure model via these schemes in different aspects. [ABSTRACT FROM AUTHOR]

The main purpose of this study was to produce abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation that represents unstable optical solitons that emerge from optical propagations through the use of birefringent fibers. These new types of soliton solutions have behaviors that are bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic and were not realized before by any other method. These new forms have been detected by using four different techniques, which are, the extended simple equation method, the Paul-Painlevé approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method. These new solitons will be arranged to create a soliton catalog with new impressive behaviors and they will contribute to future studies not only for this model but also for the optical propagations through birefringent fiber.

In our study we implement an improved modified extended tanh-function (IMETF) method for constructing new solitons and other types of solutions with NLSE having Kudryashov’s generalized nonlinear refractive index. Bright, dark and singular optical soliton solutions have been recovered for the model by this approach. Moreover, 3D and contour graphs are plotted for more illustration.

In this research article, the perturbed nonlinear Schrödinger equation (P-NLSE) is examined by utilizing two analytical methods, namely the extended modified auxiliary equation mapping and the generalized Riccati equation mapping methods. Consequently, we establish several sorts of new families of complex soliton wave solutions such as hyperbolic functions, trigonometric functions, dark and bright solitons, periodic solitons, singular solitons, and kink-type solitons wave solutions of the P-NLSE. Using the mentioned methods, the results are displayed in 3D and 2D contours for specific values of the open parameters. The obtained findings demonstrate that the implemented techniques are capable of identifying the exact solutions of the other complex nonlinear evolution equations (C-NLEEs) that arise in a range of applied disciplines.

This current research is about some new optical solitons to the time-fractional integrable generalized (2+1)-dimensional nonlinear Schrödinger (NLS) system with novel truncated M-fractional derivative. The obtained results may be used in the description of the model in fruitful way. The novel derivative operator is applied to study the aforementioned model. The achieved results are in the form of dark, bright, and combo optical solitons. The achieved solutions are also verified by using the MATHEMATICA software. The obtained solutions are explained with different plots. Modified integration methods, Expa{{\rm{Exp}}}_{a} function, extended (G′∕G)\left(G^{\prime} /G)-expansion, and extended sinh-Gordon equation expansion method are applied to achieve the results. These exact solitons suggest that these methods are effective, straight forward, and reliable compared to other methods.

In this paper, the modified simple equation method and the extended simplest equation method are applied to secure optical solitons and other solutions for Radhakrishnan-Kundu Lakshmanan equation. Bright solitons, dark solitons and singular solitons are obtained. Also, periodic solutions, singular periodic solutions, rational-type solutions and hyperbolic solutions are reported. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.

In this paper, a new evolution of polarized light ray by optical fiber in the pseudohyperbolic space ℍ02 is examined. Firstly, the characterization of the parallel transportation law associated with the geometric pseudohyperbolic phase of the light ray is given. Later, a principle nature of electric and magnetic field along with the light ray in the pseudohyperbolic space ℍ02 is defined by the geometric invariants. Finally, optical solutions of nonlinear pseudohyperbolic Schrödinger's equations governing the propagation of electromagnetic fields are successfully derived by using the traveling wave hypothesis approach. [ABSTRACT FROM AUTHOR]

The current paper recovers cubic–quartic optical solitons in fiber Bragg gratings having polynomial law of nonlinear refractive index structures. Lie symmetry analysis is carried out, starting with the basic analysis. Then, it is followed through with improved Kudryashov and generalized Arnous schemes. The parameter constraints are also identified for the existence of such solitons. Numerical surface plots support the adopted applied analysis. [ABSTRACT FROM AUTHOR]