Retrieval of soliton solutions of (1+1)-dimensional non-linear telegraph equation

Daş, Sebahat Ebru

doi:10.2298/tsci22s2801d

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…Nonlinear partial differential equations (NLPDEs) play a crucial role in understanding and predicting the behavior of complex systems in numerous scientific areas such as physics and engineering to chemistry, biology, and economics (Braun, 1983b), ), (Cinar et al, 2022), (Debnath, 2012), (Albayrak, P. 2022), (Das, S. E. 2022). These equations provide a mathematical framework to describe various physical phenomena, including fluid dynamics, heat transfer, wave propagation, and electromagnetism, etc.…”

Section: Introductionmentioning

confidence: 99%

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

ÇINAR

2024

Afyon Kocatepe University Journal of Sciences and Engineering

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This article presents an investigation for soliton solutions of the extended (2+1)-dimensional Kadomtsev–Petviashvili equation which describes wave behavior in shallow water. We utilize the unified Riccati equation expansion method. By employing the powerful method, many soliton solutions are successfully derived, and it is verified by Wolfram Mathematica that the solutions satisfy the main equation. Additionally, Matlab is utilized to generate plots and examine the properties of the obtained solitons. The results reveal that the considered equation exhibits a wide range of soliton solutions, including dark, bright, singular, and periodic solutions. This comprehensive investigation of soliton solutions for the Kadomtsev–Petviashvili equation holds significant relevance in various fields such as oceanography and nonlinear optics, contributing to practical applications.

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Section: Introductionmentioning

confidence: 99%

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

ÇINAR

2024

Afyon Kocatepe University Journal of Sciences and Engineering

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“…There are various methods for solving NLSEs. Some of the most common methods cover: new Kudryashov [20,21], unified Riccati equation expansion [22], eShGEE [23,24], the extended Kudryashov [25,26], etc.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons of improved perturbed nonlinear Schrödinger equation with cubic-quintic-septic and triple-power laws in optical metamaterials

et al. 2023

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Purpose: This paper aims to extract optical solitons of improved perturbed nonlinear Schr¨odinger equations (IP-NLSE) with cubic-quintic-septic (CQS) and a triple-power law (TP-law) using the new Kudryashov and the extended sinh-Gordon equation expansion (eShGEE) methods. Methodology: First, we apply a wave transformation to the studied equations to generate the nonlinear ordinary differential equation (NLODE) form. Next, by computing the balancing constant in the NLODE form, we use the new Kudryashov and eShGEE methods to obtain the equation’s solution in the NLODE form. We get an algebraic equation system on the NLODE by replacing the suggested solution function and its derivatives in the NLODEform. With the help of the solutions of the system, we can determine the appropriate solution sets for unknown parameters. Substituting these sets and wave transforms into the proposed solution functions by the new Kudryashov and eShGEE methods, we get the solutions for the problems under investigation. Findings: We have successfully obtained soliton solutions for the considered equations and plotted 3D and 2D graphs of the derived solution functions. In addition to obtaining the soliton solutions, we present some graphical investigation of the impact of the parameters in the considered equations.Originality: To our best knowledge, the improved perturbed nonlinear Schr¨odinger equations with CQS and a triple-power law have not been studied before. It is also innovative to examine how the equation’s parameters affect the soliton’s behavior. In this regard, the study’s findings are novel, and it is anticipated that they will advance research in the area.

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“…In recent times, since solving NLSEs has attracted great interest of researchers, a wide range of analytical methods have been put forward in the literature to solve them. The analytical methods proposed encompass a broad range of approaches, including but not limited to the unified Riccati equation expansion [36,37], F-expansion [38], Fan's method [39], Kudryashov methods [12,[40][41][42][43], exp-function [44], G ′ /G-expansion method [45], sine-Gordon expansion method [46], extended sinh-Gordon equation [47,48], the modified extended tanh function [49], and many more [50][51][52]. The dimensionless form of the Biswas-Milovic equation (BME) was introduced as follows [10]:…”

Section: Introductionmentioning

confidence: 99%

Explicit optical solitons of a perturbed Biswas-Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion

CINAR

2023

Preprint

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Objective – This paper deals with a new variant of the Biswas-Milovic equation, referred to as the perturbed Biswas-Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Methods – Utilizing a wave transformation technique on the considered Biswas-Milovic equation, and by distinguishing its real and imaginary components, we have been able to restructure the considered equation into a set of nonlinear ordinary differential equations. The solutions for these ordinary differential equations, suggested by the auxiliary equation method, include certain undetermined parameters. These solutions are then incorporated into the nonlinear ordinary differential equation, leading to the formation of an algebraic equation system by collecting like terms of the unknown function and setting their coefficients to zero. The undetermined parameters, and consequently the solutions to the Biswas-Milovic equation, are derived by resolving this system. Results – 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. Conclusion – The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems.

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Retrieval of soliton solutions of (1+1)-dimensional non-linear telegraph equation

Cited by 8 publications

References 33 publications

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

An Investigation for Soliton Solutions of the Extended (2+1)-Dimensional Kadomtsev–Petviashvili Equation

Optical solitons of improved perturbed nonlinear Schrödinger equation with cubic-quintic-septic and triple-power laws in optical metamaterials

Explicit optical solitons of a perturbed Biswas-Milovic equation having parabolic-law nonlinearity and spatio-temporal dispersion

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