Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

2010 ◽  
Vol 54 (2) ◽  
pp. 219-228 ◽  
Author(s):  
Li Qi ◽  
Zhang Da-Jun ◽  
Chen Deng-Yuan
Keyword(s):  
Inverse Scattering ◽  
Gordon Equation ◽  
Inverse Scattering Transform ◽  
Mkdv Equation ◽  
Sine Gordon Equation ◽  
Scattering Transform ◽  
Self Consistent

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.

An inverse scattering study of the radiation solution of the sine–Gordon equation

1984 ◽  
Vol 62 (7) ◽  
pp. 701-713
Author(s):  
R. H. Enns ◽  
S. S. Rangnekar
Keyword(s):  
Inverse Scattering ◽  
Evolution Equations ◽  
Gordon Equation ◽  
Wave Interaction ◽  
Nonlinear Evolution Equations ◽  
Sine Gordon Equation ◽  
Transform Method ◽  
Scattering Transform ◽  
Scattering Study ◽  
Interaction Problem

Making use of the diagrammatic approach to the inverse scattering transform method that we pioneered on the 3-wave interaction problem, we have studied the complete temporal and spatial evolution of the radiation solution of the sine–Gordon equation. The analytic results are consistent with numerical simulations as well as qualitative ideas prevalent in the literature. The extension of the diagrammatic approach to the sinh–Gordon and other nonlinear evolution equations of physical significance is also briefly discussed.

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