Bäcklund Transformations and Exact Soliton Solutions for Some Nonlinear Evolution Equations of the zs/akns Systemfn1fn1Communicated by Prof. M. Wadati.

1998 ◽  
Vol 9 (11) ◽  
pp. 1847-1855 ◽  
Author(s):  
A.H. Khater ◽  
R.S. Ibrahim ◽  
O.H. El-kalaawy ◽  
D.K. Callebaut
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
Exact Soliton Solutions

Exact Soliton Solutions of the Variable Coefficient KdV Equation with Forced Term

2014 ◽  
Vol 548-549 ◽  
pp. 1196-1200
Author(s):  
Yong Mei Bao ◽  
Siqintana Bao
Keyword(s):  
Variable Coefficient ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Nonlinear Ordinary Differential Equation ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Forced Term ◽  
Exact Soliton Solutions

In order to construct exact soliton solutions of nonlinear evolution equations with variable coefficients. By using a transformation, the variable coefficient KdV equation with forced Term is reduced to nonlinear ordinary differential equation (NLODE), after that, a number of exact solitons solutions of variable coefficient KdV equation with forced Term are obtained by using the equation shorted in NLODE. As it showed above, this kind of method can be applied in solving a large number of nonlinear evolution equations.

Auto-Bäcklund Transformations Derived via the Implicit C-D Pair

2012 ◽  
Vol 268-270 ◽  
pp. 1345-1348
Author(s):  
Xiao Li Wang ◽  
Jian Qin Mei ◽  
Zhen Hua Wu
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Bäcklund Transformations ◽  
New Approach ◽  
Backlund Transformations

By the implicit C-D pairs, a new approach to auto-B¨acklund transformations of nonlinear evolution equations is presented in this paper. The auto-B¨acklund transformations for combined KdV and MKdV equations are obtained by this approach.

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