Scattering Amplitudes for Multi-indexed Extensions of Soliton Potential and Extended KdV Integer Solitons

TL;DR

This paper develops methods to analyze scattering problems for extended soliton potentials and applies these to generate higher integer KdV solitons using inverse scattering techniques.

Contribution

It introduces a novel approach to compute scattering for multi-indexed soliton potentials via Darboux transformations and extends the inverse scattering method to generate higher KdV solitons.

Findings

Successfully calculated scattering problems for extended soliton potentials.

Generated an infinite set of higher integer KdV solitons.

Demonstrated the effectiveness of Darboux transformations in this context.

Abstract

We calculate quantum mechanical scattering problems for multi-indexed extensions of soliton potential by Darboux transformations in terms of pseudo virtual wavefunctions. As an application, we calculate infinite set of higher integer KdV solitons by the inverse scattering transform method of KdV equation.