On the Bäcklund Transformations of KDV Equations and Modified KDV Equations

1989 ◽  
pp. 45-50
Author(s):  
Shiing-shen Chern ◽  
Chia-kuei Peng
Keyword(s):  
Bäcklund Transformations ◽  
Kdv Equations ◽  
Backlund Transformations ◽  
Modified Kdv Equations

Riccati-type Bäcklund transformations of nonisospectral and generalized variable-coefficient KdV equations

2014 ◽  
Vol 23 (3) ◽  
pp. 030506
Author(s):  
Yun-Qing Yang ◽  
Yun-Hu Wang ◽  
Xin Li ◽  
Xue-Ping Cheng
Keyword(s):  
Variable Coefficient ◽  
Bäcklund Transformations ◽  
Kdv Equations ◽  
Backlund Transformations

scholarly journals Two Kinds of Darboux-Bäcklund Transformations for theq-Deformed KdV Hierarchy with Self-Consistent Sources

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Hongxia Wu ◽  
Liangjuan Gao ◽  
Jingxin Liu ◽  
Yunbo Zeng
Keyword(s):  
Soliton Solution ◽  
Pseudodifferential Operators ◽  
Bäcklund Transformation ◽  
Bäcklund Transformations ◽  
Backlund Transformation ◽  
Kdv Hierarchy ◽  
Kdv Equations ◽  
Backlund Transformations ◽  
Self Consistent

Two kinds of Darboux-Bäcklund transformations (DBTs) are constructed for theq-deformedNth KdV hierarchy with self-consistent sources (q-NKdVHSCS) by using theq-deformed pseudodifferential operators. Note that one of the DBTs provides a nonauto Bäcklund transformation for twoq-deformedNth KdV equations with self-consistent sources (q-NKdVESCS) with different degree. In addition, the soliton solution to the first nontrivial equation ofq-KdVHSCS is also obtained.

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

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