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arXiv · 2507.03966

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

Michał Kowalczyk·Yvan Martel
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Abstract

The asymptotic stability of the black and dark solitons of the one-dimensional Gross-Pitaevskii equation was proved by B\'ethuel, Gravejat and Smets (Ann. Sci. \'Ec. Norm. Sup\'er. 48 (2015)) and Gravejat and Smets (Proc. Lond. Math. Soc. 111 (2015)), using a rigidity property in the vicinity of solitons. We provide an alternate proof of the Liouville theorems in the above articles using a factorization identity for the linearized operator which trivializes the spectral analysis.

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Michał Kowalczyk, Yvan Martel. 2025-07-05. A new proof of a Liouville theorem for the one dimensional Gross-Pitaevskii equation. https://arxiv.org/abs/2507.03966

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