IST of KPII equation for perturbed multisoliton solutions

TL;DR

This paper formulates the scattering problem for the heat operator with perturbed multisoliton potentials, introduces spectral data, and linearizes the KP-II equation for perturbed soliton solutions, advancing understanding of their dynamics.

Contribution

It develops a framework for analyzing perturbed multisoliton solutions of the KP-II equation via scattering theory and spectral data, including their time evolution.

Findings

Spectral data properties are characterized for perturbed multisoliton potentials.

The initial value problem for perturbed KP-II solutions is linearized.

A method for analyzing the dynamics of perturbed solitons is established.

Abstract

The Direct and the Inverse Scattering Problems for the heat operator with a potential being a perturbation of an arbitrary $N$ soliton potential are formulated. We introduce Jost solutions and spectral data and present their properties. Then, giving the time evolution of the spectral data, the initial value problem of the Kadomtsev-Petviashvili II equation for a solution describing $N$ solitons perturbed by a generic smooth fast decaying potential is linearized.