New exact solutions for a generalized variable-coefficient KdV equation

2008 ◽  
Vol 69 (8) ◽  
pp. 2763-2770 ◽  
Author(s):  
R. Sabry ◽  
W.F. El-Taibany
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Kdv Equation ◽  
New Exact Solutions

The Multiple Exact Solutions for the Variable Coefficient KdV Equation

2014 ◽  
Vol 513-517 ◽  
pp. 4474-4477
Author(s):  
Lin Tian ◽  
Jia Qing Miao
Keyword(s):  
Exact Solutions ◽  
Variable Coefficient ◽  
Kdv Equation ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions ◽  
Auxiliary Differential Equation Method ◽  
Differential Equation Method

The auxiliary differential equation method has recently been proposed ,It is introduced to construct more new exact solutions for the variable coefficient KdV equations. As a result , hyperbolic function solutions, trigonometric function solutions, and elliptic function solutions rational function solutions with parameters are obtained.

scholarly journals New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yusuf Pandir ◽  
Halime Ulusoy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
New Exact Solutions

We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE), we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

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