Soliton solutions and Bäcklund transformations of a (2 + 1)-dimensional nonlinear evolution equation via the Jaulent–Miodek hierarchy

2014 ◽  
Vol 78 (4) ◽  
pp. 2341-2347 ◽  
Author(s):  
De-Yin Liu ◽  
Bo Tian ◽  
Yan Jiang ◽  
Wen-Rong Sun
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Bäcklund Transformations ◽  
Backlund Transformations

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 Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

scholarly journals Soliton Solutions and Conservation Laws of a (3+1)-Dimensional Nonlinear Evolution Equation

2019 ◽  
Vol 135 (3) ◽  
pp. 539-545
Author(s):  
M. Ekici ◽  
A. Sonmezoglu ◽  
A. Rashid Adem ◽  
Qin Zhou ◽  
Zitong Luan ◽  
...  
Keyword(s):  
Evolution Equation ◽  
Conservation Laws ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions

The Properties of Bilinear Derivative

2014 ◽  
Vol 543-547 ◽  
pp. 1905-1908
Author(s):  
Ju Mei Zhang ◽  
Hong Lun Wang ◽  
Wen Yan Cui
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Learning And Teaching ◽  
Derivative Method ◽  
Nonlinear Science ◽  
Definition Of

Bilinear derivative method is widely used in calculating multi-soliton solutions of some nonlinear evolution equation. The paper proves some frequently used properties of bilinear derivative from the perspective of the definition of bilinear derivative, hoping to be useful for learning and teaching in nonlinear science.

Sign in / Sign up

Export Citation Format

Share Document