The direct scattering problem for perturbed Kadomtsev-Petviashvili multi line solitons

TL;DR

This paper rigorously analyzes the direct scattering problem for perturbed KP multi-line solitons, advancing the understanding of their stability and scattering properties within the Grassmannian framework.

Contribution

It provides a complete rigorous analysis of the direct scattering problem for perturbed Grassmannian KP solitons, which was previously not fully addressed.

Findings

Established a rigorous framework for the direct scattering problem

Enhanced understanding of stability properties of perturbed KP solitons

Extended the inverse scattering method to perturbed multi-line solitons

Abstract

Regular Kadomtsev-Petviashvili II (KPII) line solitons have been investigated and classified successfully by the Grassmannians. The inverse scattering method provides a promising and powerful approach to study the stability properties of $\textrm{Gr}(N, M)_{> 0}$ KP solitons. In this paper, we complete rigorous analysis for the direct scattering problem of perturbed $\textrm{Gr}(N, M)_{> 0}$ KP solitons}.