Residual symmetry, n th Bäcklund transformation, and soliton‐cnoidal wave interaction solution for the combined modified KdV–negative‐order modified KdV equation

2019 ◽  
Vol 43 (3) ◽  
pp. 1253-1266 ◽  
Author(s):  
Wenguang Cheng ◽  
Deqin Qiu ◽  
Tianzhou Xu
Keyword(s):  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Wave Interaction ◽  
Cnoidal Wave ◽  
Backlund Transformation ◽  
Interaction Solution ◽  
Residual Symmetry ◽  
Negative Order ◽  
Modified Kdv Equation

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.

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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