Work

A new proof of a Liouville theorem for the one dimensional Gross–Pitaevskii equation

Year: 2025

Type: article

Abstract: The asymptotic stability of the black and dark solitons of the one-dimensional Gross–Pitaevskii equation was proved by Béthuel, Gravejat and Smets ( Ann. Sci. Éc. Norm. Supér. , 2015), and Gravejat and Smets ( Proc. Lond. Math. Soc. , 2015), using a rigidity property in the vicinity of solitons. We provide an alternate proof of the Liouville theorems in those two articles, using a factorization identity for the linearized operator which trivializes the spectral analysis.

Source: Comptes Rendus Mathématique

DOI: 10.5802/crmath.799

Authors: Michał Kowalczyk, Yvan Martel

Institutions: Centre National de la Recherche Scientifique, Center for Mathematical Modeling, University of Chile

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Universidad de Chile, Agencia Nacional de Investigación y Desarrollo

Awards: ASYMPTOTIC STABILITY OF SOME DEFOCUSING DISPERSIVE PROBLEMS IN THEIR ENERGY SPACE, CENTER FOR MATHEMATICAL MODELING (CMM)