A nonlocal variable coefficient KdV equation: Bäcklund transformation and nonlinear waves

2020 ◽  
Vol 135 (1) ◽  
Author(s):  
Xi-zhong Liu
Keyword(s):  
Nonlinear Waves ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Backlund Transformation

BÄCKLUND TRANSFORMATION AND ANALYTIC SOLUTIONS FOR A GENERALIZED VARIABLE-COEFFICIENT MODIFIED KORTEWEG–DE VRIES MODEL FROM FLUID DYNAMICS AND PLASMAS

2008 ◽  
Vol 19 (11) ◽  
pp. 1659-1671 ◽  
Author(s):  
FU-WEI SUN ◽  
YI-TIAN GAO ◽  
CHUN-YI ZHANG ◽  
XIAO-GE XU
Keyword(s):  
Fluid Dynamics ◽  
External Force ◽  
Variable Coefficient ◽  
Bäcklund Transformation ◽  
Solitary Wave Solution ◽  
Kdv Equation ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Backlund Transformation ◽  
De Vries

We investigate a generalized variable-coefficient modified Korteweg–de Vries model with perturbed factor and external force (vc-GmKdV) describing fluid dynamics and space plasmas. In this paper, we propose an extended variable-coefficient balancing-act method (Evc-BAM), which is concise and straightforward, to obtain the generalized analytic solutions including solitary wave solution of the vc-GmKdV model with symbolic computation. Meanwhile, using the Evc-BAM, we obtain an auto-Bäcklund transformation for the vc-GmKdV model on the relevant constraint conditions of the coefficient functions. Using the given auto-Bäcklund transformation, the solutions of special equations for the vc-GmKdV model are also obtained as the variable-coefficient Korteweg–de Vries (vc-KdV) equation, the generalized KdV equation with perturbed factor and external force (GKdV), the variable-coefficient modified Korteweg–de Vries (vc-mKdV) equation, and the variable-coefficient cylindrical modified Korteweg–de Vries (vc-cmKdV) equation, respectively.

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

2016 ◽  
Vol 27 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Zi-Jian Xiao ◽  
Bo Tian ◽  
Hui-Ling Zhen ◽  
Jun Chai ◽  
Xiao-Yu Wu
Keyword(s):  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Backlund Transformation
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