Singular solutions of the KdV equation and the inverse scattering method

1985 ◽  
Vol 31 (6) ◽  
pp. 3264-3279 ◽  
Author(s):  
V. A. Arkad'ev ◽  
A. K. Pogrebkov ◽  
M. K. Polivanov
Keyword(s):  
Inverse Scattering ◽  
Kdv Equation ◽  
Inverse Scattering Method ◽  
Singular Solutions ◽  
Scattering Method ◽  
The Kdv Equation

SUPERSYMMETRY, REFLECTIONLESS SYMMETRIC POTENTIALS AND THE INVERSE METHOD

1990 ◽  
Vol 05 (09) ◽  
pp. 1763-1772 ◽  
Author(s):  
B. BAGCHI
Keyword(s):  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Inverse Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Inverse Scattering Method ◽  
Wave Functions ◽  
Scattering Method ◽  
De Vries

The role of inverse scattering method is illustrated to examine the connection between the multi-soliton solutions of Korteweg-de Vries (KdV) equation and discrete eigenvalues of Schrödinger equation. The necessity of normalization of the Schrödinger wave functions, which are constructed purely from a supersymmetric consideration is pointed out.

Verifying the Soliton Solutions to the Fifth Order KdV Equation by Ordinary Inverse Scattering Method

2014 ◽  
Vol 1051 ◽  
pp. 1000-1003 ◽  
Author(s):  
Chao Ma ◽  
Jin Chun He
Keyword(s):  
Inverse Scattering ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Fifth Order ◽  
Jost Solution

The Jost solution of the fifth order KdV equation derived from inverse scattering transformation in Gel’fand-Levitan-Marchenko formalism satisfy the both two compatibility equations. Therefore, the soliton solutions to the fifth order KdV equation can be verified theoretically.

Spatially Inhomogeneous Plasma with Negative Ions and Modified KdV Equation with x Dependent Term

1986 ◽  
Vol 41 (4) ◽  
pp. 601-604
Author(s):  
R. K. Roychoudhury ◽  
Sikha Bhattacharrya
Keyword(s):  
Inverse Scattering ◽  
Kdv Equation ◽  
Inhomogeneous Plasma ◽  
Negative Ions ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Spatially Inhomogeneous ◽  
Dependent Term ◽  
Modified Kdv Equation ◽  
Perturbation Solutions

We have derived a modified KdV equation with x dependent term in the case of a spatially inhomogeneous plasma using the stretched co-ordinate system by Asano. Exact and perturbation solutions derived from inverse scattering method are discussed.

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