scholarly journals Multiple Soliton Solutions of the Sawada-Kotera Equation with a Nonvanishing Boundary Condition and the Perturbed Korteweg de Vries Equation by Using the Multiple Exp-Function Scheme

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Abdullahi Rashid Adem ◽  
Mohammad Mirzazadeh ◽  
Qin Zhou ◽  
Kamyar Hosseini
Keyword(s):  
Boundary Condition ◽  
Perturbation Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Systematic Technique ◽  
Multiple Soliton Solutions ◽  
De Vries

The Sawada-Kotera equation with a nonvanishing boundary condition, which models the evolution of steeper waves of shorter wavelength than those depicted by the Korteweg de Vries equation, is analyzed and also the perturbed Korteweg de Vries (pKdV) equation. For this goal, a capable method known as the multiple exp-function scheme (MEFS) is formally utilized to derive the multiple soliton solutions of the models. The MEFS as a generalization of Hirota’s perturbation method actually suggests a systematic technique to handle nonlinear evolution equations (NLEEs).

Noncommutative coupled complex modified Korteweg–de Vries equation: Darboux and binary Darboux transformations

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950054
Author(s):  
H. Wajahat A. Riaz
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Nonlinear Evolution Equations ◽  
Order Effects ◽  
Darboux Transformations ◽  
De Vries ◽  
Higher Order Effects

Higher-order nonlinear evolution equations are important for describing the wave propagation of second- and higher-order number of fields in optical fiber systems with higher-order effects. One of these equations is the coupled complex modified Korteweg–de Vries (ccmKdV) equation. In this paper, we study noncommutative (nc) generalization of ccmKdV equation. We present Darboux and binary Darboux transformations (DTs) for the nc-ccmKdV equation and then construct its Quasi-Grammian solutions. Further, single and double-hump soliton solutions of first- and second-order are given in commutative settings.

DEFORMED KORTEWEG-DE VRIES EQUATION WITH SYMBOLIC COMPUTATION

2001 ◽  
Vol 12 (09) ◽  
pp. 1335-1344 ◽  
Author(s):  
YI-TIAN GAO ◽  
BO TIAN
Keyword(s):  
Symbolic Computation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Analytic Solutions ◽  
Nonlinear Evolution Equations ◽  
Important Class ◽  
Exact Analytic Solutions ◽  
Engineering Sciences ◽  
De Vries

The Korteweg-de Vries-typed equations are the most important class of nonlinear evolution equations, with numerous applications in physical and engineering sciences. In this paper, for the deformed Korteweg-de Vries equation of the form [Formula: see text], we make use of computerized symbolic computation and obtain several families of new exact analytic solutions, some of which are solitonic.

scholarly journals Multiple Soliton Solutions for a New Generalization of the Associated Camassa-Holm Equation by Exp-Function Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yao Long ◽  
Yinghui He ◽  
Shaolin Li
Keyword(s):  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Mathematical Tool ◽  
Multiple Soliton Solutions ◽  
Holm Equation

The Exp-function method is generalized to construct N-soliton solutions of a new generalization of the associated Camassa-Holm equation. As a result, one-soliton, two-soliton, and three-soliton solutions are obtained, from which the uniform formulae of N-soliton solutions are derived. It is shown that the Exp-function method may provide us with a straightforward, effective, and alternative mathematical tool for generating N-soliton solutions of nonlinear evolution equations in mathematical physics.

scholarly journals The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations

2021 ◽  
Vol 22 ◽  
pp. 103979
Author(s):  
Nauman Raza ◽  
Muhammad Hamza Rafiq ◽  
Melike Kaplan ◽  
Sunil Kumar ◽  
Yu-Ming Chu
Keyword(s):  
Local Time ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
The Unified Method ◽  
Unified Method

scholarly journals A note on improved F -expansion method combined with Riccati equation applied to nonlinear evolution equations

2014 ◽  
Vol 1 (2) ◽  
pp. 140038 ◽  
Author(s):  
Md. Shafiqul Islam ◽  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
Antonio Mastroberardino
Keyword(s):  
Riccati Equation ◽  
Wave Equations ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Expansion Method ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Wave Equations ◽  
Travelling Wave Solutions

The purpose of this article is to present an analytical method, namely the improved F -expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

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