A novel generalized Kudryashov method for exact solutions of nonlinear evolution equations

2017 ◽  
Author(s):  
Murat Koparan ◽  
Melike Kaplan ◽  
Ahmet Bekir ◽  
Ozkan Guner
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

The shock peakon wave solutions of the general Degasperis–Procesi equation

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Lijuan Qian ◽  
Raghda A. M. Attia ◽  
Yuyang Qiu ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Stability Property ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dynamical Behavior ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Different Types ◽  
The Stability

This research paper applies the modified Khater method and the generalized Kudryashov method to the general Degasperis–Procesi (DP) equation, which is used to describe the dynamical behavior of the shallow water outflows. Some shock peakon wave solutions are obtained by using these methods. Moreover, some figures are sketched for these solutions to explain more physical properties of the general DP equation and to figure out the coincidence between different types of obtained solutions. The stability property by using the features of the Hamiltonian system is tested to some obtained solutions to show their ability for applying in the model’s applications. The obtained solutions were verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows their power and effectiveness for applying to many different forms of the nonlinear evolution equations with an integer and fractional order.

scholarly journals New Jacobi Elliptic Function Solutions for the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yun-Mei Zhao
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function

A generalized(G′/G)-expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution equations in mathematical physics.

Sign in / Sign up

Export Citation Format

Share Document