Minimizing travelling waves for the Gross-Pitaevskii equation on ℝ × \mathbbT

2022/02/18 by André de Laire, de Laire, André, Philippe Gravejat +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2202.09411

openalex publication_date 2022/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Gross-Pitaevskii equation in dimension two with periodic conditions in one direction, or equivalently on the product space ℝ × \mathbbT_L where L > 0 and \mathbbT_L = ℝ / L ℤ. We focus on the variational problem consisting in minimizing the Ginzburg-Landau energy under a fixed momentum constraint. We prove that there exists a threshold value for L below which minimizers are the one-dimensional dark solitons, and above which no minimizer can be one-dimensional.

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