Optical Soliton Solutions Research Articles

Integrable Akbota equation: conservation laws, optical soliton solutions and stability analysis

Integrable Akbota equation: conservation laws, optical soliton solutions and stability analysis

Optical exact soliton solutions of nonlinear optical transmission equation using two explicit methods

Optical exact soliton solutions of nonlinear optical transmission equation using two explicit methods

Distinct optical soliton solutions to the fractional Hirota Maccari system through two separate strategies

The real-world phenomena are characterized with the assistance of nonlinear evolution equations. The present study explores interesting and effective appropriate solitary wave solutions of Hirota Maccari system (HMs) in the sense of beta fractional derivative. This nonlinear model is popular for its significant role in explaining the phenomena relating to plasma physics, optical fibers, and marine engineering. The solitons arise in the mentioned model state how the waves maintain amplitude and shape during the propagation in fiber which is important for long distance data transmission and fiber optic technology. We impose the improved auxiliary equation and improved tanh approaches on the suggested model and accumulate numerous wave solutions in a successful manner. The well-furnished solutions are characterized through graphical representations in 3D, 2D and contour profiles to illustrate the dynamic nature of nonlinear optical solitons. The effects of the wave phase are brought out with the assistance of multiple 2D outlines. A variety of solitons are noticed alongside peakon, kink, anti-kink, singular kink, cuspon, singular bell, anti-bell, bell, periodic and compacton etc. N-shape soliton and M-shape soliton are also constructed in this study. A comparison view of the achieved solutions with the existing results of literature is drawn for highlighting the novelty and diversity of the present entire work. The achieved optical solitons alongside other solutions might be significant to analyze the nonlinear phenomena in signal processing and optic fiber communication.

Optical soliton solutions: the evolution with changing fractional-order derivative in Biswas–Arshed and Schrödinger Kerr law equations

Optical soliton solutions: the evolution with changing fractional-order derivative in Biswas–Arshed and Schrödinger Kerr law equations

Unveiling optical soliton solutions and bifurcation analysis in the space–time fractional Fokas–Lenells equation via SSE approach

The space–time fractional Fokas–Lenells (STFFL) equation serves as a fundamental mathematical model employed in telecommunications and transmission technology, elucidating the intricate dynamics of nonlinear pulse propagation in optical fibers. This study employs the Sardar sub-equation (SSE) approach within the STFFL equation framework to explore uncharted territories, uncovering a myriad of optical soliton solutions (OSSs) and conducting a thorough analysis of their bifurcations. The discovered OSSs encompass a diverse array, including bright-dark, periodic, multiple bright-dark solitons, and various other types, forming a captivating spectrum. These solutions reveal an intricate interplay among bright-dark solitons, complex periodic sequences, rhythmic breathers, coexistence of multiple bright-dark solitons, alongside intriguing phenomena like kinks, anti-kinks, and dark-bell solitons. This exploration, built upon meticulous literature review, unveils previously undiscovered wave patterns within the dynamic framework of the STFFL equation, significantly expanding the theoretical understanding and paving the way for innovative applications. Utilizing 2D, contour, and 3D diagrams, we illustrate the influence of fractional and temporal parameters on these solutions. Furthermore, comprehensive 2D, 3D, contour, and bifurcation analysis diagrams scrutinize the nonlinear effects inherent in the STFFL equation. Employing a Hamiltonian function (HF) enables detailed phase-plane dynamics analysis, complemented by simulations conducted using Python and MAPLE software. The practical implications of the discovered OSS solutions extend to real-world physical events, underlining the efficacy and applicability of the SSE scheme in solving time–space nonlinear fractional differential equations (TSNLFDEs). Hence, it is crucial to acknowledge the SSE technique as a direct, efficient, and reliable numerical tool, illuminating precise outcomes in nonlinear comparisons.

Dynamic behavior of optical self-control soliton in a liquid crystal model

The Paraxial Model, a foundational concept in optics, provides a simplified yet effective approach to understanding the behavior of light in optical systems. This research investigates optical soliton solutions within the truncated time M-fractional Paraxial wave equation using the extended tanh method and the modified extended tanh method. Addressing the challenge of fractional order, we employ the shortened M-fractional derivative to eliminate it from the governing model, facilitating a detailed analysis. Through strategic manipulation of free parameters, soliton solutions are expressed in terms of hyperbolic and trigonometric functions, revealing a spectrum of soliton phenomena such as Lump soliton, rough wave, periodic soliton, and king wave for specific parameter values that are connected to the dispersal effect, the Kerr non-linearity effect and the diffraction effect of the governing equation. To enhance the understanding of these solutions, we utilize Matlab for graphical representations, providing a visual interpretation of the intricate dynamics. This study not only uncovers diverse soliton behaviors in the context of fractional wave equations but also offers valuable insights into their formation and complexity, bridging theoretical analysis with computational visualization.

Some optical soliton solutions with bifurcation analysis of the paraxial nonlinear Schrödinger equation

Some optical soliton solutions with bifurcation analysis of the paraxial nonlinear Schrödinger equation

Optical soliton solutions for the parabolic nonlinear Schrödinger Hirota’s equation incorporating spatiotemporal dispersion via the tanh method linked with the Riccati equation

Optical soliton solutions for the parabolic nonlinear Schrödinger Hirota’s equation incorporating spatiotemporal dispersion via the tanh method linked with the Riccati equation

The Perturbed Chen–Lee–Liu Equation: Diverse Optical Soliton Solutions and Other Wave Solutions

The objective of the present study is to extract the optical soliton solutions (OSSs) of the perturbed Chen–Lee–Liu equation by exerting three techniques, which are the extended Wang’s direct mapping method, tanh/coth function method and the Subequation method. Various OSSs, including the dark, bright, and singular soliton solutions, as well as other wave solutions, such as the singular periodic and algebraic solitary wave solutions, are successfully found. By assigning the appropriate parameters, the dynamic characteristics of the attained solutions are depicted graphically via the Mathematica software. The outcomes confirm that the methods are highly effective for constructing the OSSs and can also be adopted to investigate the other PDEs in optics.

Optical soliton solutions for Lakshmanan-Prosezain- Daniel model using three different methods

Optical soliton solutions for Lakshmanan-Prosezain- Daniel model using three different methods

Contraction of variational principle and optical soliton solutions for two models of nonlinear Schrödinger equation with polynomial law nonlinearity

<abstract><p>Our study analyzes the two models of the nonlinear Schrödinger equation (NLSE) with polynomial law nonlinearity by powerful and comprehensible techniques, such as the variational principle method and the amplitude ansatz method. We will derive the functional integral and the Lagrangian of these equations, which illustrate the system's dynamic. The solutions of these models will be extracted by selecting the trial ansatz functions based on the Jost linear functions, which are continuous at all intervals. We start with the Jost function that has been approximated by a piecewise linear function with a single nontrivial variational parameter in three cases from a region of a rectangular box, then use this trial function to obtain the functional integral and the Lagrangian of the system without any loss. After that, we approximate this trial function by piecewise linear ansatz function in two cases of the two-box potential, then approximate it by quadratic polynomials with two free parameters rather than a piecewise linear ansatz function, and finally, will be approximated by the tanh function. Also, we utilize the amplitude ansatz method to extract the new solitary wave solutions of the proposed equations that contain bright soliton, dark soliton, bright-dark solitary wave solutions, rational dark-bright solutions, and periodic solitary wave solutions. Furthermore, conditions for the stability of the solutions will be submitted. These answers are crucial in applied science and engineering and will be introduced through various graphs such as 2D, 3D, and contour plots.</p></abstract>

Exploring unconventional optical soliton solutions for a novel $ \mathfrak{q} $-deformed mathematical model

<abstract><p>This paper presents a significant contribution in the form of a new general equation, namely the $ \mathfrak{q} $-deformed equation or the $ \mathfrak{q} $-deformed tanh-Gordon equation. The introduction of this novel equation opens up new possibilities for modeling physical systems that exhibit violated symmetries. By employing the $ (G'/G) $ expansion method, we have successfully derived solitary wave solutions for the newly defined $ \mathfrak{q} $-deformed equation under specific parameter regimes. These solutions provide valuable insights into the behavior of the system and its dynamics. To further validate the obtained analytical results, the numerical solution of the $ \mathfrak{q} $-deformed equation has been constructed by using the finite difference method. This numerical approach ensures the accuracy and reliability of the findings. To facilitate a comprehensive understanding of the results, we have included two- and three-dimensional tables and figures, which provide visual representations and comparisons between the analytical and numerical solutions. These graphical illustrations enhance the clarity and interpretation of the obtained data. The significance of the $ \mathfrak{q} $-deformation lies in its ability to model physical systems that exhibit deviations from standard symmetry properties, such as extensivity. This type of modeling is increasingly relevant in various fields, as it allows for a more accurate representation of real-world phenomena.</p></abstract>

Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes

<abstract><p>This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schrödinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schrödinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algorithms are implemented to investigate the optical solitons with the governing model. These techniques are the Weierstrass-type projective Riccati equation expansion method, the addendum to Kudryashov's method, and the new mapping method. The solutions obtained include various solitons, such as bright, dark, and straddled solitons. Additionally, the paper reports hyperbolic solutions and Weierstrass-type doubly periodic solutions. These solutions are novel and have never been reported before. Visual depictions of some selected solitons illustrate these solutions' dynamic behavior and wave structure.</p></abstract>

Analytical discovery of dark soliton lattices in (2+1)-dimensional generalized fractional Kundu-Mukherjee-Naskar equation

<p>This research explored optical soliton solutions for the (2+1)-dimensional generalized fractional Kundu-Mukherjee-Naskar equation (gFKMNE), which is a nonlinear model for explaining pulse transmission in communication structures and optical fibers. Two enhanced variants of $ (\frac{G'}{G}) $-expansion method were employed, namely, extended $ (\frac{G'}{G}) $-expansion method and the generalized $ (r+\frac{G'}{G}) $-expansion method, based on the wave transformation of the model into integer-order nonlinear ordinary differential equations (NODEs). By assuming a series-form solution for the resultant NODEs, these strategic methods further translated them into a system of nonlinear algebraic equations. Solving these equations provided optical soliton solutions for gFKMNE using the Maple-13 tool. Through 3D and contour visuals, it was revealed that the constructed soliton solutions are periodically arranged in the optical medium, forming dark soliton lattices. These dark soliton lattices are significant in several domains, such as optical signal processing, optical communications, and nonlinear optics.</p>

Numerous optical soliton solutions of the Triki–Biswas model arising in optical fiber

A model condition for the propagation of ultrashort pulses in optical fiber frameworks could be established through the extensive generalization of the nonlinear Schrödinger equation introduced by Triki and Biswas. This study uses two significant and effective trustworthy methods to examine the Triki–Biswas (TB) equation. Sardar Subequation Methods (SSM) and the generalized Kudryashov (KUD) method generate solutions for trigonometric, hyperbolic, exponential, and rational functions. These approaches are specifically designed for handling solitary wave patterns, dark-singular-mixed solitons, combined dark-bright solitons, singletons, bright solitons, exponential and rational functions, as well as periodic solitons. All of these solution classes contribute to the physical dynamics of outcomes. These findings represent an innovative extension of the soliton domain within the TB model and are being reported for the first time in our investigation. In addition, Mathematica simulations are used to display the 3D and 2D graphs to explain the identified solutions’ physical dynamics.

Exploring optical soliton solutions of a self-focusing nonlinear Schrödinger equation by two effective techniques

Exploring optical soliton solutions of a self-focusing nonlinear Schrödinger equation by two effective techniques

Optical dark, singular and bright soliton solutions with dual-mode fourth-order nonlinear Schrödinger equation involving different nonlinearities

This research article investigates the dynamic characteristics of solitary waves within a medium exhibiting weak nonlinearity in dual-mode. Firstly, the three models are converted to dual-mode. The primary focus is to investigate the behavior of solitary waves in a system described by a fourth-order nonlinear Schrödinger (NLS) equation, which incorporates Kerr nonlinearity, weak nonlocality, parabolic law nonlinearity and diffraction. By employing ansatz methods, the study successfully derives various localized waveforms, including bright, dark and singular solitons, based on the governing model. The examination extends to investigating the influence of nonlocality and power coefficients on dynamics of bright, dark and singular solitons. The findings presented in this article represent a crucial advancement in understanding the generation of solitary waves in nonlinear media. As the examined model finds application in various fields such as plasma physics, Bose-Einstein condensates and others, these findings not only enhance our theoretical understanding but also pave the way for potential practical applications and the advancement of innovative technologies.

Optical solitons for the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise

This investigation of the current work presents the dispersive concatenation model that integrates the spatio-temporal dispersion and the effect of multiplicative white noise in the Itô sense. The study aims to secure stochastic optical soliton solutions within this framework. To achieve this purpose, we implemented the enhanced Kudryashov technique and the new projective Riccati equations strategy. Initially, the traveling wave transform hypothesis was applied to convert the stochastic model into its nonlinear ordinary differential equation form, encompassing real and imaginary components with emerging the related parametric restrictions. Subsequently, we introduced the enhanced Kudryashov and the new projective Riccati equations techniques successfully employed in analyzing the generated nonlinear ordinary differential equation. By utilizing the appropriate solution sets, which encompass variables with unknown values and necessary transformations, we have derived many stochastic optical soliton-type solutions for the model. Detailed discussions for the dynamics of some selected soliton solutions are presented with the supporting of the 3D and 2D graphs that illustrate the white noise effect on these solitons.

Assorted optical soliton solutions of the nonlinear fractional model in optical fibers possessing beta derivative

The nonlinear Chen-Lee-Liu (CLL) equation is an important mathematical model that is employed in the evaluation of optical fiber communication systems. It considers several factors such as noise, dispersion, and nonlinearity that might affect the signal quality and data transmission rates in optical fiber networks. The design of optical fiber systems may be optimized by using the CLL model. In this paper, we have examined adequate soliton solutions that can be applied to the optics of the CLL model with a beta derivative utilizing the auxiliary equation and advanced generalized -expansion approaches. The bell-shaped, periodic, and other soliton-like properties are displayed in the numerical simulations of the resultant solutions and the necessary forms demonstrated the structure, propagation, and impact of the fractional parameter. The findings of this study show that the applied methodologies are dependable, effective, and competent to create optical soliton solutions for additional complex wave equations in optical fiber communication.

Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation

This study is based on the Lie group method for the nonlinear elastic structural element equation (ESE Equation). We obtain a three-dimensional Lie algebra. By utilizing this Lie algebra a four-dimensional optimal system is constructed. The governing ESE Equation is converted to nonlinear ordinary differential equations (ODEs) via symmetry reduction. We use a modified auxiliary equation (MAE) procedure to deal with nonlinear ODEs. These ODEs reveal the dynamics of the periodic and soliton solutions. We obtain soliton solutions through rational, trigonometric, and hyperbolic functions. Wolfram Mathematica simulations vividly illustrate the wave characteristics of the derived solutions, affirming their properties as singular periodic solutions, a singular solution, an optical dark soliton solution, and a singular soliton solution. We also obtain the local conservation laws by a new conservation theorem introduced by Ibragimov.