Multi-indexed Extensions of Soliton Potential and Extended Integer Solitons of KdV Equation

TL;DR

This paper introduces a method to generate higher integer KdV soliton solutions using multi-indexed extensions of reflectionless potentials, solvable via inverse scattering techniques.

Contribution

It develops a novel approach to construct higher integer soliton solutions of the KdV equation through multi-indexed extensions, expanding the class of exactly solvable potentials.

Findings

Infinite set of initial profiles for higher integer KdV solitons derived.

Solutions are exactly solvable for Schrödinger and Gel'fand-Levitan-Marchenko equations.

Method extends the framework of reflectionless soliton potentials.

Abstract

We calculate infinite set of initial profiles of higher integer KdV solitons, which are both exactly solvable for the Schrodinger equation and for the Gel'fand-Levitan-Marchenko equation in the inverse scattering transform 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.