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arXiv · 2610.24261

Global well-posedness and orbital stability of the Gross--Pitaevskii branch in a coupled defocusing Schrödinger system

Michał Kowalczyk·Jarosław Mederski·Isidora Miranda
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Abstract

We consider a one-dimensional coupled defocusing Schrödinger system with a nonzero background in its first component and finite mass in its second component. We prove global well-posedness in the full energy space, together with conservation of energy, bright mass, and total untwisted momentum. For all nonnegative coupling coefficients, every subsonic Gross--Pitaevskii soliton with vanishing second component is orbitally stable against perturbations of both components, including the zero-speed black soliton. At nonzero speed the proof uses a fixed energy--momentum functional augmented by the conserved bright mass. At zero speed it uses weighted coercivity and a local real lift of the momentum. We also identify the sharp threshold for positivity of the unaugmented bright energy and explain why this threshold is not a necessary condition for orbital stability.

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Michał Kowalczyk, Jarosław Mederski, Isidora Miranda. 2026-10-16. Global well-posedness and orbital stability of the Gross--Pitaevskii branch in a coupled defocusing Schrödinger system. https://arxiv.org/abs/2610.24261

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