Stability of Kadomtsev-Petviashvili multi-line solitons

TL;DR

This paper establishes a rigorous inverse scattering theory for perturbed Kadomtsev-Petviashvili multi-line solitons, demonstrating their stability and advancing understanding of multi-dimensional integrable systems.

Contribution

It provides the first rigorous inverse scattering framework for multi-dimensional integrable systems with both continuous and discrete data, without degenerate support.

Findings

Proves the long-standing inverse scattering theory for KP multi-line solitons.

Establishes $L^ Infty$ stability of these solitons.

Handles non-degenerate continuous scattering data support.

Abstract

We prove the long-standing inverse scattering theory (IST) of perturbed Kadomtsev Petviashvili multi-line solitons. Our work is the first rigorous IST of a multi-dimensional integrable system when both continuous and discrete scattering data are present, and the support of continuous scattering data does not degenerate into contours in the complex plane. As an application, an $L^\infty$-stability theorem of the Kadomtsev Petviashvili multi-line solitons is justified.