Optical Soliton Solutions for Nonlinear Evolution Equations in Mathematical Physics by Using the Extended (G'/G) Expansion Function Method

2017 ◽  
Vol 14 (2) ◽  
pp. 979-990 ◽  
Author(s):  
KhaledA. Gepreel ◽  
TaherA. Nofal ◽  
NehalS. Al-Sayali
Keyword(s):  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Optical Soliton ◽  
Nonlinear Evolution Equations

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.

ANALYTICAL TREATMENT OF SOME PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MATHEMATICAL PHYSICS BY USING THEExp-FUNCTION METHOD

2011 ◽  
Vol 25 (22) ◽  
pp. 2965-2981 ◽  
Author(s):  
MEHDI DEHGHAN ◽  
JALIL MANAFIAN ◽  
ABBAS SAADATMANDI
Keyword(s):  
Function Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Periodic Structures ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Computational System ◽  
Analytical Treatment ◽  
Zk Equation ◽  
Solitary Solutions

The Exp -function method with the aid of symbolic computational system can be used to obtain the generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics. In this paper, we study the analytic treatment of the Zakharov–Kuznetsov (ZK) equation, the modified ZK equation, and the generalized forms of these equations. Exact solutions with solitons and periodic structures are obtained.

Analytical solutions of the fifth-order time fractional nonlinear evolution equations by the unified method

2021 ◽  
Author(s):  
Abdul Majeed ◽  
Muhammad Naveed Rafiq ◽  
Mohsin Kamran ◽  
Muhammad Abbas ◽  
Mustafa Inc
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Important Goal ◽  
Sense Of Time ◽  
Fifth Order ◽  
The Unified Method ◽  
Unified Method

This key purpose of this study is to investigate soliton solution of the fifth-order Sawada–Kotera and Caudrey–Dodd–Gibbon equations in the sense of time fractional local [Formula: see text]-derivatives. This important goal is achieved by employing the unified method. As a result, a number of dark and rational soliton solutions to the nonlinear model are retrieved. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behavior. The results demonstrate that the presented approach is more effective in solving issues in mathematical physics and other fields.

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