On multi-solitons for coupled lowest Landau level equations

Laurent Thomann (1)

1 IECL - Institut Élie Cartan de Lorraine

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 Schrödinger equation with harmonic potential perturbed by a time-dependent potential.

Mots clés: growth of Sobolev norms; multi-solitons; progressive waves; stationary solutions; Nonlinear Schrödinger equation; Lowest Landau Level

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Thomann. On multi-solitons for coupled lowest Landau level equations. 2021. ⟨hal-03419797v2⟩