Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations

2017 ◽  
Author(s):  
Burcu Ayhan ◽  
M. Naci Ozer ◽  
Ahmet Bekir
Keyword(s):  
Evolution Equations ◽  
Multiple Scales ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Multiple Scales Analysis

Method of Multiple Scales and Travelling Wave Solutions for (2+1)-Dimensional KdV Type Nonlinear Evolution Equations

2016 ◽  
Vol 71 (8) ◽  
pp. 703-713 ◽  
Author(s):  
Burcu Ayhan ◽  
M. Naci Özer ◽  
Ahmet Bekir
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Kdv Type Equations

AbstractIn this article, we applied the method of multiple scales for Korteweg–de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The$\left( {{{G'} \over G}} \right)$-expansion methods and the$\left( {{{G'} \over G},{\rm{ }}{1 \over G}} \right)$-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).

The Functional Variable Method to Find New Exact Solutions of the Nonlinear Evolution Equations with Dual-Power-Law Nonlinearity

2020 ◽  
Vol 21 (3-4) ◽  
pp. 249-257 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Javad Vahidi ◽  
Asim Zafar ◽  
Ahmet Bekir
Keyword(s):  
Power Law ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Functional Variable ◽  
Functional Variable Method ◽  
Dual Power

AbstractIn this work, we established new travelling wave solutions for some nonlinear evolution equations with dual-power-law nonlinearity namely the Zakharov–Kuznetsov equation, the Benjamin–Bona–Mahony equation and the Korteweg–de Vries equation. The functional variable method was used to construct travelling wave solutions of nonlinear evolution equations with dual-power-law nonlinearity. The travelling wave solutions are expressed by generalized hyperbolic functions and the rational functions. This method presents a wider applicability for handling nonlinear wave equations.

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