scholarly journals Multi-indexed extensions of soliton potential and extended integer solitons of KdV equation

2015 ◽  
Vol 30 (24) ◽  
pp. 1550115
Author(s):  
Choon-Lin Ho ◽  
Jen-Chi Lee
Keyword(s):  
Schrödinger Equation ◽  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Inverse Scattering Transform ◽  
Scattering Transform ◽  
Exactly Solvable ◽  
De Vries ◽  
Infinite Set

We calculate infinite set of initial profiles of higher integer Korteweg–de Vries (KdV) solitons, which are both exactly solvable for the Schrödinger equation and for the Gel’fand–Levitan–Marchenko (GLM) equation in the inverse scattering transform (IST) method of KdV equation. The calculation of these higher integer soliton solutions is based on the recently developed multi-indexed extensions of the reflectionless soliton potential.

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.

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