Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources

2002 ◽  
Vol 38 (6) ◽  
pp. 641-644 ◽  
Author(s):  
Zeng Yun-Bo ◽  
Shao Yi-Jun ◽  
Ma Wen-Xiu
Keyword(s):  
Darboux Transformations ◽  
Integral Type ◽  
Self Consistent ◽  
Mkdv Hierarchy

The Eigenfunctions and Exact Solutions of Discrete mKdV Hierarchy with Self-Consistent Sources via the Inverse Scattering Transform

2015 ◽  
Vol 7 (5) ◽  
pp. 663-674 ◽  
Author(s):  
Q. Li ◽  
J. B. Zhang ◽  
D. Y. Chen
Keyword(s):  
Exact Solutions ◽  
Spectral Problem ◽  
Inverse Scattering ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
The Self ◽  
Scattering Transform ◽  
Self Consistent ◽  
Exact Soliton Solutions ◽  
Mkdv Hierarchy

AbstractAnother form of the discrete mKdV hierarchy with self-consistent sources is given in the paper. The self-consistent sources is presented only by the eigenfunctions corresponding to the reduction of the Ablowitz-Ladik spectral problem. The exact soliton solutions are also derived by the inverse scattering transform.

scholarly journals Integration of the Harry Dym equation with an integral type source

2021 ◽  
Vol 31 (2) ◽  
pp. 285-295
Author(s):  
G.U. Urazboev ◽  
A.K. Babadjanova ◽  
D.R. Saparbaeva
Keyword(s):  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Data ◽  
Evolutionary Equation ◽  
Integral Type ◽  
Self Consistent ◽  
The Cauchy Problem ◽  
Nonlinear Evolutionary Equation ◽  
Dym Equation ◽  
Harry Dym Equation

In the work, we deduce the evolution of scattering data for a spectral problem associated with the nonlinear evolutionary equation of Harry Dym with a self-consistent source of integral type. The obtained equalities completely determine the scattering data for any $t$, which makes it possible to apply the method of the inverse scattering problem to solve the Cauchy problem for the Harry Dym equation with an integral type source.

scholarly journals A Integrable Generalized Super-NLS-mKdV Hierarchy, Its Self-Consistent Sources, and Conservation Laws

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Hanyu Wei ◽  
Tiecheng Xia
Keyword(s):  
Conservation Laws ◽  
Lie Superalgebra ◽  
Hamiltonian Form ◽  
Self Consistent ◽  
Set Up ◽  
Mkdv Hierarchy

A generalized super-NLS-mKdV hierarchy is proposed related to Lie superalgebra B(0,1); the resulting supersoliton hierarchy is put into super bi-Hamiltonian form with the aid of supertrace identity. Then, the super-NLS-mKdV hierarchy with self-consistent sources is set up. Finally, the infinitely many conservation laws of integrable super-NLS-mKdV hierarchy are presented.

scholarly journals Self-Consistent Sources for Integrable Equations Via Deformations of Binary Darboux Transformations

2016 ◽  
Vol 106 (8) ◽  
pp. 1139-1179 ◽  
Author(s):  
Oleksandr Chvartatskyi ◽  
Aristophanes Dimakis ◽  
Folkert Müller-Hoissen
Keyword(s):  
Darboux Transformations ◽  
Integrable Equations ◽  
Self Consistent
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