Bäcklund transformations, nonlinear superposition principle, multisoliton solutions and conserved quantities for the « boomeron » nonlinear evolution equation

1976 ◽  
Vol 16 (14) ◽  
pp. 434-438 ◽  
Author(s):  
F. Calogero ◽  
A. Degasperis
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Superposition Principle ◽  
Bäcklund Transformations ◽  
Conserved Quantities ◽  
Nonlinear Superposition ◽  
Backlund Transformations ◽  
Multisoliton Solutions

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 The Multisoliton Solutions for the (2+1)-Dimensional Sawada-Kotera Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Zhenhui Xu ◽  
Hanlin Chen ◽  
Wei Chen
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
High Dimensional ◽  
Wave Solutions ◽  
Solitary Solutions ◽  
Ansatz Approach ◽  
Multisoliton Solutions

Applying bilinear form and extended three-wavetype of ansätz approach on the (2+1)-dimensional Sawada-Kotera equation, we obtain new multisoliton solutions, including the double periodic-type three-wave solutions, the breather two-soliton solutions, the double breather soliton solutions, and the three-solitary solutions. These results show that the high-dimensional nonlinear evolution equation has rich dynamical behavior.

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