Applications of an Improved (GʹG) -expansion Method to Nonlinear PDEs in Mathematical Physics

2009 ◽  
Author(s):  
E. M. E. Zayed ◽  
Shorog Al-Joudi ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Pdes

An Improved (GʹG)-expansion Method for Solving Nonlinear PDEs in Mathematical Physics

2010 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Shorog Al-Joudi ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Pdes

An Improved (GʹG)-expansion Method for Solving Nonlinear PDEs in Mathematical Physics

2010 ◽  
Author(s):  
Elsayed M. E. Zayed ◽  
Shorog Al-Joudi ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Pdes

scholarly journals The (G′/G,1/G)-Expansion Method and Its Applications to Find the Exact Solutions of Nonlinear PDEs for Nanobiosciences

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
E. M. E. Zayed ◽  
K. A. E. Alurrfi
Keyword(s):  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Periodic Wave ◽  
Nonlinear Pdes ◽  
Mathematical Tool ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Powerful Mathematical Tool

The two-variable (G′/G,1/G)-expansion method is employed to construct exact traveling wave solutions with parameters of nanobiosciences partial differential equation. When the parameters are replaced by special values, the solitary wave solutions and the periodic wave solutions of this equation have been obtained from the traveling waves. This method can be thought of as the generalization of well-known originalG′/G-expansion method proposed by M. Wang et al. It is shown that the two-variable (G′/G,1/G)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics. Comparison between our results and the well-known results is given.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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.

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