Optical Solitary Wave Solutions Research Articles

Construction of optical solitary wave solutions and their propagation for Kuralay system using tanh-coth and energy balance method

In this article, we study the complex coupled Kuralay system (CKS), which have many applications in different field such as ferromagnetic material and fiber optics. We implement an analytical method, namely, the tanh–coth method to considered system to formulate a system of algebraic equations. Solving the obtained system, we acquire different traveling wave solutions that are expressed in term of hyperbolic tangent functions and hyperbolic cotangent functions. Also, we employ the energy balance technique to the selected model to sort out the behavior of traveling wave solutions. By this method, we obtain periodic wave solution that are expressed in term of cosine function. In order to show the graphical presentation of the acquired solitary waves solutions, 3D and 2D curve are created by selecting well-suited parametric values via Mathematica.

Solitary waves of the generalized Zakharov equations via integration algorithms

<abstract><p>In many applications, the investigation of traveling wave solutions is essential in obtaining an accurate description of the dynamical behavior of most physical phenomena. The exact solutions to nonlinear equations can provide more physical descriptions and insightful details for many problems of practical interest. This paper focuses on investigating the solitary wave solutions of the generalized Zakharov equations (GZEs) by using four integration algorithms, namely, the modified $ (g'/g^{2}) $-expansion method, the modified $ (g') $-expansion method, the generalized simple ($ w/g $)-expansion method, and the addendum to Kudryashov's method. The GZEs have been widely used to describe the propagation of Langmuir waves in the field of plasma physics. The efficiency and simplicity of these methods are evaluated based on their application to GZEs, which have yielded multiple new optical solitary wave solutions in the form of rational, trigonometric, and hyperbolic functions. By using a suitable wave transformation, the coupled nonlinear partial differential equations are converted into ordinary differential equations. The derived optical solutions are graphically depicted in $ 2 $D and $ 3 $D plots for some specific parameter values. The traveling wave solutions discovered in the current study constitute just one example of the desired solutions that may enable the exploration of the physical properties of many complex systems and could also contribute greatly to improving our understanding of many interesting natural phenomena that arise in different applications, including plasma physics, fluid mechanics, protein chemistry, wave propagation, and optical fibers.</p></abstract>

Optical Dromions for Spatiotemporal Fractional Nonlinear System in Quantum Mechanics

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.

Optical solitary wave solutions in generalized determinant form for Kundu–Eckhaus equation

The Kundu–Eckhaus (KE) equation describes the propagation of ultra-short femtosecond pulses in optical fibers. In this paper, on the basis of Hirota bilinear form of KE equation, a complex matrix is introduced into the differential relation satisfied by determinant elements. By constructing relations among the matrix elements, the solution in generalized double Wronskian determinant form for the KE equation is derived. When the complex matrix introduced in the differential relation of the determinant elements take diagonal matrix and Jordan block matrix respectively, the soliton solutions and Jordan block solutions of the KE equation are obtained and propagation situations are discussed via different parameters.

Dynamics of Diverse Optical Solitary Wave Solutions to the Biswas–Arshed Equation in Nonlinear Optics

Dynamics of Diverse Optical Solitary Wave Solutions to the Biswas–Arshed Equation in Nonlinear Optics

Explore Optical Solitary Wave Solutions of the kp Equation by Recent Approaches

The study of nonlinear evolution equations is a subject of active interest in different fields including physics, chemistry, and engineering. The exact solutions to nonlinear evolution equations provide insightful details and physical descriptions into many problems of interest that govern the real world. The Kadomtsev–Petviashvili (kp) equation, which has been widely used as a model to describe the nonlinear wave and the dynamics of soliton in the field of plasma physics and fluid dynamics, is discussed in this article in order to obtain solitary solutions and explore their physical properties. We obtain several new optical traveling wave solutions in the form of trigonometric, hyperbolic, and rational functions using two separate direct methods: the (w/g)-expansion approach and the Addendum to Kudryashov method (akm). The nonlinear partial differential equation (nlpde) is reduced into an ordinary differential equation (ode) via a wave transformation. The derived optical solutions are graphically illustrated using Maple 15 software for specific parameter values. The traveling wave solutions discovered in this work can be viewed as an example of solutions that can empower us with great flexibility in the systematic analysis and explanation of complex phenomena that arise in a variety of problems, including protein chemistry, fluid mechanics, plasma physics, optical fibers, and shallow water wave propagation.

Sasa-Satsuma’s Dynamical Equation and Optical Solitary Wave Solutions

Sasa-Satsuma’s Dynamical Equation and Optical Solitary Wave Solutions

Bifurcation of new optical solitary wave solutions for the nonlinear long-short wave interaction system via two improved models of $$(\frac{G'}{G})$$ expansion method

Bifurcation of new optical solitary wave solutions for the nonlinear long-short wave interaction system via two improved models of $$(\frac{G'}{G})$$ expansion method

Stability analysis, solitary wave and explicit power series solutions of a (2 + 1)-dimensional nonlinear Schrödinger equation in a multicomponent plasma

PurposeThe purpose of this paper is to study the stability analysis and optical solitary wave solutions of a (2 + 1)-dimensional nonlinear Schrödinger equation, which are derived from a multicomponent plasma with nonextensive distribution.Design Methodology ApproachBased on the ansatz and sub-equation theories, the authors use a direct method to find stability analysis and optical solitary wave solutions of the (2 + 1)-dimensional equation.FindingsBy considering the ansatz method, the authors successfully construct the bright and dark soliton solutions of the equation. The sub-equation method is also extended to find its complexitons solutions. Moreover, the explicit power series solution is also derived with its convergence analysis. Finally, the influences of each parameter on these solutions are discussed via graphical analysis.Originality ValueThe dynamics of these solutions are analyzed to enrich the diversity of the dynamics of high-dimensional nonlinear Schrödinger equation type nonlinear wave fields.

New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method

This article presents soliton solutions to a generalized nonlinear Fokas-Lenells equation via the Sine-Gordon expansion method. To uncover the clear picture of the gained solutions, the two and three-dimensional figures for the solutions are given. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.

Exploring the dark and singular soliton solutions of Biswas–Arshed model with full nonlinear form

In this paper, the optical solitons of two nonlinear forms, namely Kerr type and power law form, of Biswas–Arshed model are studied. To construct optical solitary wave solutions of the aforementioned model, the modified extended tanh expansion method was used successful. As a consequence, many new optical solitons including, dark, singular, dark/singular, and periodic soliton solutions are retrieved and verified through MATHEMATICA.

MODULATION INSTABILITY AND OPTICAL SOLITONS OF RADHAKRISHNAN-KUNDU-LAKSHMANAN MODEL

This paper studies the solitons of Radhakrishnan-Kundu-Lakshma- nan (RKL) model with power law nonlinearity. The modified simple equation method and $ \exp(-\varphi({q}) $) method are presented as integration mechanisms. Dark, bright, singular and periodic soliton solutions are extracted as well as the constraint conditions for their existence. A prized discussion on the stability of these soliton profiles on the basis of index of the power law nonlinearity is also carried out with the help of physical description of solutions. The integration techniques have been proved to be extremely efficient and robust to find new optical solitary wave solutions for various nonlinear evolution equations describing optical pulse propagation. Moreover, using linear stability analysis, modulation instability of the RKL model is studied. Different effects contributing to the modulation instability spectrum gain are analyzed.

APPROXIMATE ADOMIAN SOLUTIONS TO THE BRIGHT OPTICAL SOLITARY WAVES OF THE CHEN-LEE-LIU EQUATION

The present paper examines the Chen–Lee–Liu (CLL) equation numerically. The equation is an important type of the Derivative Nonlinear Schrodinger (DNLS) equations that describe the propagation of pulse in optical fibers. The optical solitary wave solutions of the CLL equation comprises of the recently obtained bright solitons via ansatz method. However, in this paper, we employ the promising Adomian Decomposition Method (ADM) to further demonstrate its efficiency in solving different types of Schrodinger equations. The method reveals amazing approximate solutions with minimal error as shown in the respective comparison tables and various plots depicted.

Dispersive optical solitary wave solutions of strain wave equation in micro-structured solids and its applications

The new technique of modified extended mapping technique is an important, prevailing and direct Mathematical tool for constructing exact solutions in the form of traveling waves of non-linear evolution equations (NLEEs) in applied science and engineering. The dispersive effect of the combination of the microstructure and nonlinearity of the material can produce solitary waves. In micro-structured solids, the wave propagation in microstructured materials is modeled by strain wave mechanics equation. In this paper, several new solutions of strain wave dynamical model for micro-structured solids are obtained by using the strongly modified extended mapping technique. We obtain exact waves solutions, including solitons, solitary waves, kinks and anti-kink solitary waves, periodic and rational solutions which have key applications and useful for researchers to understand the phenomena. The three-dimensional graphs and contour plots of some solutions attained in this study are drawn by giving the suitable values of the parameters used to understand the solutions of physical interpretation. The model stability is studied via modulational instability analysis and dispersion relation is derived which verify that these solutions are stable. The computational work and the results demonstrate that the new extended technique is effective and influential.

Optical solitary wave and elliptic function solutions of the Fokas–Lenells equation in the presence of perturbation terms and its modulation instability

In this paper, we study the Fokas–Lenells (F-L) equation in the presence of perturbation terms and we construct exact solutions. The modified extended direct algebraic method (MEDAM) is utilized, and soliton solutions, solitary wave solutions and elliptic function solutions are achieved. The physical meaning of the geometrical shapes for some of the obtained results is investigated for various choices of the free parameters that appear in the results. The stability of the model is investigated by using the standard linear stability analysis, which verifies that the exact solutions are stable. The achieved solutions and computational work show that the current method is powerful and influential.

A study of optical wave propagation in the nonautonomous Schrödinger-Hirota equation with power-law nonlinearity

Abstract This paper investigates the nonautonomous Schrodinger-Hirota equation with power-law nonlinearity via the Unified Method. New nonautonomous optical wave solutions are obtained in polynomial function solutions type. Among these solutions: the optical solitary, optical soliton and optical elliptic wave solutions. The physical explanations and the dynamical behavior of the solutions describing the wave propagation in optical fibers are discussed and analyzed for different choices of the arbitrary functions in the solutions.

Grey and black optical solitary waves, and modulation instability analysis to the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

ABSTRACTThis paper addresses the nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity and perturbation terms in optical fibre. A class of grey and black optical solitary wave solutions of this equation are retrieved by adopting an appropriate solitary wave ansatz solution. These types of solitary waves play a vital role in understanding various physical phenomena in nonlinear systems. This lead to a constraint condition on the solitary wave parameters which must hold for the solitary waves to exist. Moreover, the modulation instability (MI) analysis of the model is studied by employing the concept of linear-stability analysis (LSA) and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviours of the equation.

Optical Solitary Wave Solutions of the Space-Time Fractional Modified Equal-Width Equation and their Applications

Optical Solitary Wave Solutions of the Space-Time Fractional Modified Equal-Width Equation and their Applications

Optical solitary waves and conservation laws to the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation

This work studies the hyperbolic nonlinear Schrödinger equation (H-NLSE) in (2 + 1)-dimensions. The model describes the evolution of the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics, and also governs the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics. A class of gray and black optical solitary wave solutions of the H-NLSE are reported by adopting an appropriate solitary wave ansatz solution. Moreover, classification of conservation laws (Cls) to the H-NLSE is implemented using the multipliers approach. Some physical interpretations and analysis of the results obtained are also presented.

New optical solitary wave solutions of Fokas-Lenells equation in presence of perturbation terms by a novel approach

A variety of new optical waves solutions of the Fokas-Lenells equation in presence of perturbation terms is investigated. A new approach is used, namely the generalized exponential function method. The physical meaning of the geometrical structures for some of these solutions is discussed for different choices of the free parameters present in the solutions. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations.