Asymptotic stability of N-soliton states of NLS

TL;DR

This paper proves the existence and asymptotic stability of multi-soliton solutions for the focusing nonlinear Schrödinger equation, demonstrating that solutions tend to a combination of N non-colliding solitons over time.

Contribution

It establishes the asymptotic stability of N-soliton states under spectral assumptions, advancing understanding of long-term behavior of solutions to the focusing NLS.

Findings

Existence of multi-soliton solutions under spectral conditions

Asymptotic stability of these solutions as time approaches infinity

Solutions resemble a linear combination of N non-colliding solitons asymptotically

Abstract

The focusing nonlinear Schrodinger equation possesses special non-dispersive solitary type solutions, solitons. Under certain spectral assumptions we show existence and asymptotic stability of solutions with the asymptoic profile (as time goes to infinity) of a linear combination of N non-colliding solitons.