Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation

1989 ◽  
Vol 36 (1-2) ◽  
pp. 189-197 ◽  
Author(s):  
V.A. Arkadiev ◽  
A.K. Pogrebkov ◽  
M.C. Polivanov
Keyword(s):  
Inverse Scattering ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Transform Method ◽  
Scattering Transform

scholarly journals Inverse scattering transform for new mixed spectral Ablowitz-Kaup-Newell-Segur equations

2020 ◽  
Vol 24 (4) ◽  
pp. 2437-2444
Author(s):  
Sheng Zhang ◽  
Caihong You
Keyword(s):  
Inverse Scattering ◽  
Spectral Parameter ◽  
Analytical Methods ◽  
Linear Problem ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Time Varying ◽  
Spatial Structures ◽  
New Exact Solutions ◽  
Scattering Transform

The inverse scattering transform plays a very important role in promoting the development of analytical methods to solve non-linear PDE exactly. In this paper, new and more general mixed spectral Ablowitz-Kaup-Newell-Segur equations are derived and solved by embedding a novel time-varying spectral parameter in-to an associated linear problem and the inverse scattering transform. As a result, new exact solutions and n-soliton solutions are obtained. To gain more insights into the embedded spectral parameter and the obtained solutions, some dynamical evolutions, and spatial structures are simulated. It is shown that the derived Ablowitz-Kaup-Newell-Segur equations are Lax integrable and the obtained soliton solutions possess time-varying amplitudes.

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.

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