Exact Solutions, Symmetry Reductions, Painlevé Test and Bäcklund Transformations of A Coupled KdV Equation

2017 ◽  
Vol 68 (4) ◽  
pp. 417
Author(s):  
XU Min-Hui ◽  
JIA Man
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Painlevé Test ◽  
Symmetry Reductions ◽  
Backlund Transformations ◽  
Coupled Kdv Equation

scholarly journals Bäcklund Transformation and New Exact Solutions of the Sharma-Tasso-Olver Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Lin Jianming ◽  
Ding Jie ◽  
Yuan Wenjun
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Analytic Study ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Backlund Transformation ◽  
New Exact Solutions ◽  
Backlund Transformations ◽  
Painleve Analysis

The Sharma-Tasso-Olver (STO) equation is investigated. The Painlevé analysis is efficiently used for analytic study of this equation. The Bäcklund transformations and some new exact solutions are formally derived.

Painlevé Test, Bäcklund Transformation and Consistent Riccati Expansion Solvability for two Generalised Cylindrical Korteweg-de Vries Equations with Variable Coefficients

2018 ◽  
Vol 73 (3) ◽  
pp. 207-213 ◽  
Author(s):  
Rehab M. El-Shiekh
Keyword(s):  
Vries Equation ◽  
Dusty Plasmas ◽  
Variable Coefficients ◽  
Bäcklund Transformations ◽  
Painlevé Test ◽  
New Exact Solutions ◽  
Backlund Transformations ◽  
Integrability Conditions ◽  
De Vries ◽  
Consistent Riccati Expansion

AbstractIn this paper, the integrability of the (2+1)-dimensional cylindrical modified Korteweg-de Vries equation and the (3+1)-dimensional cylindrical Korteweg-de Vries equation with variable coefficients arising in dusty plasmas in its generalised form was studied by two different techniques: the Painlevé test and the consistent Riccati expansion solvability. The integrability conditions and Bäcklund transformations are constructed. By using Bäcklund transformations and the solutions of the Riccati equation many new exact solutions are found for the two equations in this study. Finally, the application of the obtained solutions in dusty plasmas is investigated.

scholarly journals Bäcklund Transformations between the KdV Equation and a New Nonlinear Evolution Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Xifang Cao
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
The Other ◽  
Bäcklund Transformations ◽  
Backlund Transformations ◽  
The Kdv Equation ◽  
New Equation

We first give a Bäcklund transformation from the KdV equation to a new nonlinear evolution equation. We then derive two Bäcklund transformations with two pseudopotentials, one of which is from the KdV equation to the new equation and the other from the new equation to itself. As applications, by applying our Bäcklund transformations to known solutions, we construct some novel solutions to the new equation.

scholarly journals Bäcklund transformations for several cases of a type of generalized KdV equation

2004 ◽  
Vol 2004 (63) ◽  
pp. 3369-3377
Author(s):  
Paul Bracken
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Backlund Transformation ◽  
Generalized Kdv Equation ◽  
Backlund Transformations ◽  
De Vries ◽  
Derivative Term

An alternate generalized Korteweg-de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are generated and studied.

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