On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations

Andrew Comech; Scipio Cuccagna

doi:10.3934/dcds.2020316

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2021, Volume 41, Issue 3: 1225-1270. Doi: 10.3934/dcds.2020316

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On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations

Andrew Comech^1, and
Scipio Cuccagna^2, ,

1.
Texas A & M University, College Station, TX, USA, Institute for Information Transmission Problems, Moscow, Russia
2.
University of Trieste, Trieste 34127, Italy

^* Corresponding author: Scipio Cuccagna
^* Corresponding author: Scipio Cuccagna

Received: July 2019

Revised: November 2019

Early access: August 2020

Published: March 2021

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Abstract

We extend to a specific class of systems of nonlinear Schrödinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation coordinates and the novelty, compared to the scalar NLS, is the fact that the group of symmetries of the system is non-commutative.

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Mathematics Subject Classification: Primary:35B35, 35B40, 35C08, 35Q41;Secondary:37K40.

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