scholarly journals Soliton solutions of an integrable nonlocal modified Korteweg–de Vries equation through inverse scattering transform

2017 ◽  
Vol 453 (2) ◽  
pp. 973-984 ◽  
Author(s):  
Jia-Liang Ji ◽  
Zuo-Nong Zhu
Keyword(s):  
Inverse Scattering ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Scattering Transform ◽  
De Vries

scholarly journals Inverse scattering transform for a supersymmetric Korteweg-de Vries equation

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 677-684
Author(s):  
Sheng Zhang ◽  
Caihong You
Keyword(s):  
Exact Solutions ◽  
Inverse Scattering ◽  
Evolution Equations ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Grassmann Algebra ◽  
Inverse Scattering Transform ◽  
Linear Evolution ◽  
Scattering Transform ◽  
De Vries

In this paper, the inverse scattering transform is extended to a super Korteweg-de Vries equation with an arbitrary variable coefficient by using Kulish and Zeitlin?s approach. As a result, exact solutions of the super Korteweg-de Vries equation are obtained. In the case of reflectionless potentials, the obtained exact solutions are reduced to soliton solutions. More importantly, based on the obtained results, an approach to extending the scattering transform is proposed for the supersymmetric Korteweg-de Vries equation in the 1-D Grassmann algebra. It is shown the the approach can be applied to some other supersymmetric non-linear evolution equations in fluids.

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