Hetero-Bäcklund Transformation, Bilinear Forms and N Solitons for a Generalized Three-Coupled Korteweg-de Vries System

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Xin-Yi Gao ◽  
Yong-Jiang Guo ◽  
Wen-Rui Shan
Keyword(s):  
Bäcklund Transformation ◽  
Bilinear Forms ◽  
Backlund Transformation ◽  
De Vries

Bäcklund transformation according to Gerdzikov and Kullish for the Korteweg–de Vries equation

1982 ◽  
Vol 60 (11) ◽  
pp. 1599-1606 ◽  
Author(s):  
Henri-François Gautrin
Keyword(s):  
Vries Equation ◽  
Bäcklund Transformation ◽  
Bäcklund Transformations ◽  
Scattering Parameters ◽  
Backlund Transformation ◽  
Specific Change ◽  
Backlund Transformations ◽  
De Vries

A study of solutions of the Gel'fand–Levitan equation permits one to establish new Bäcklund transformations for the Korteweg–de Vries equation. To a specific change in the scattering parameters, there corresponds a family of Bäcklund transformations. A means to construct these transformations is presented.

scholarly journals Nonlocal Symmetry and Bäcklund Transformation of a Negative-Order Korteweg–de Vries Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jinxi Fei ◽  
Weiping Cao ◽  
Zhengyi Ma
Keyword(s):  
Vries Equation ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Nonlocal Symmetry ◽  
Linear Superposition ◽  
Residual Symmetry ◽  
Negative Order ◽  
De Vries ◽  
Finite Transformation ◽  
New Variables

The residual symmetry of a negative-order Korteweg–de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the original nKdV equation is extended into an enlarged system by introducing four new variables. By using Lie’s first theorem, we obtain the finite transformation for the localized residual symmetry. Furthermore, we localize the linear superposition of multiple residual symmetries and construct n-th Bäcklund transformation for this nKdV equation in the form of the determinants.

Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science

2020 ◽  
Vol 34 (25) ◽  
pp. 2050226 ◽  
Author(s):  
Yu-Qi Chen ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
He Li ◽  
Xue-Hui Zhao ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Atmospheric Science ◽  
Backlund Transformation ◽  
Atmospheric Flow ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Nonlinearity Dispersion

For a variable-coefficient Korteweg–de Vries equation in a lake/sea, two-layer liquid, atmospheric flow, cylindrical plasma or interactionless plasma, in this paper, we derive the bilinear Bäcklund transformation, non-isospectral Ablowitz–Kaup–Newell–Segur system and infinite conservation laws for the wave amplitude under certain constraints among the external force, dissipation, nonlinearity, dispersion and perturbation.

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.

Sign in / Sign up

Export Citation Format

Share Document