The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula

2020 ◽  
Vol 53 (29) ◽  
pp. 294003 ◽  
Author(s):  
Gaihua Wang ◽  
Q P Liu ◽  
Hui Mao
Keyword(s):  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Nonlinear Superposition ◽  
Holm Equation ◽  
Nonlinear Superposition Formula

scholarly journals A Bäcklund transformation and nonlinear superposition formula for the Lotka-Volterra hierarchy

2002 ◽  
Vol 44 (1) ◽  
pp. 121-128 ◽  
Author(s):  
Xing-Biao Hu ◽  
Johan Springael
Keyword(s):  
Bäcklund Transformation ◽  
Lax Pair ◽  
Volterra Equations ◽  
Backlund Transformation ◽  
Nonlinear Superposition ◽  
Bilinear Bäcklund Transformation ◽  
Nonlinear Superposition Formula

AbstractA hierarchy of bilinear Lotka-Volterra equations with a unified structure is proposed. The bilinear Bäcklund transformation for this hierarchy and the corresponding canonical Lax pair are obtained. Furthermore, the nonlinear superposition formula is proved rigorously.

A Darboux Transformation for Ito Equation

2016 ◽  
Vol 71 (5) ◽  
pp. 427-431 ◽  
Author(s):  
Xiaoxing Niu ◽  
Mengxia Zhang ◽  
Shuqiang Lv
Keyword(s):  
Darboux Transformation ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Nonlinear Superposition ◽  
The One ◽  
Nonlinear Superposition Formula ◽  
Ito Equation

AbstractA system proposed by Ito is reconsidered. The corresponding Darboux transformation is presented explicitly. The resulted Bäcklund transformation is shown to be equivalent to the one found by Hirota. Also, a nonlinear superposition formula, which is of differential-algebraic, is obtained.

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