On multi-solitons for coupled Lowest Landau Level equations

TL;DR

This paper studies multi-soliton solutions for coupled nonlinear Lowest Landau Level equations, proving their existence, uniqueness, and stability, and demonstrating their relevance to dynamics in perturbed linear Schrödinger equations.

Contribution

It introduces the first existence and stability results for multi-solitons in coupled Lowest Landau Level equations, with implications for quantum dynamics.

Findings

Existence of multi-solitons with localized errors

Uniqueness of these multi-soliton solutions

Long-time stability of traveling wave sums

Abstract

We consider a coupled system of nonlinear Lowest Landau Level equations. We first show the existence of multi-solitons with an exponentially localised error term in space, and then we prove a uniqueness result. We also show a long time stability result of the sum of traveling waves having all the same speed, under the condition that they are localised far away enough from each other. Finally, we observe that these multi-solitons provide examples of dynamics for the linear Schr{\"o}dinger equation with harmonic potential perturbed by a time-dependent potential.