Applications of Nonlinear Partial Differential Equations in Mathematical Physics

1965 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mathematical Physics ◽  
Partial Differential

scholarly journals Improved General Mapping Deformation Method for Nonlinear Partial Differential Equations in Mathematical Physics

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Khaled A. Gepreel
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Jacobi Elliptic Function ◽  
Deformation Method ◽  
Partial Differential ◽  
General Mapping

We use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method to construct some of the generalized Jacobi elliptic solutions for some nonlinear partial differential equations in mathematical physics via the generalized nonlinear Klein-Gordon equation and the classical Boussinesq equations. As a result, some new generalized Jacobi elliptic function-like solutions are obtained by using this method. This method is more powerful to find the exact solutions for nonlinear partial differential equations.

scholarly journals A Note about the General Meromorphic Solutions of the Fisher Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Jian-ming Qi ◽  
Qiu-hui Chen ◽  
Wei-ling Xiong ◽  
Wen-jun Yuan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mathematical Physics ◽  
Fisher Equation ◽  
Complex Method ◽  
Mathematical Tool ◽  
Meromorphic Solutions ◽  
Partial Differential ◽  
Powerful Mathematical Tool

We employ the complex method to obtain the general meromorphic solutions of the Fisher equation, which improves the corresponding results obtained by Ablowitz and Zeppetella and other authors (Ablowitz and Zeppetella, 1979; Feng and Li, 2006; Guo and Chen, 1991), andwg,i(z)are new general meromorphic solutions of the Fisher equation forc=±5i/6.Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics.

scholarly journals Study of coupled nonlinear partial differential equations for finding exact analytical solutions

2015 ◽  
Vol 2 (7) ◽  
pp. 140406 ◽  
Author(s):  
Kamruzzaman Khan ◽  
M. Ali Akbar ◽  
H. Koppelaar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Partial Differential ◽  
Exact Analytical Solutions

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced ( G ′/ G )-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Sign in / Sign up

Export Citation Format

Share Document