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arXiv · 1804.09875

Multi-vortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials

Yong Liu·Juncheng Wei
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Abstract

For $N\leq34,$ we construct traveling waves with small speed for the Gross-Pitaevskii equation, by gluing $N(N+1)/2$ pairs of degree $\pm1$ vortices of the Ginzburg-Landau equation. The location of these vortices is symmetric in the plane and determined by the Adler-Moser polynomials, which has its origin in the study of Calogero-Moser system and rational solutions of the KdV equation. The construction still works for $N>34$, under the additional assumption that the corresponding Adler-Moser polynomial has no repeated root. It is expected that this assumption holds for any $N\in\mathbb{N}$.

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Yong Liu, Juncheng Wei. 2018-04-26. Multi-vortex traveling waves for the Gross-Pitaevskii equation and the Adler-Moser polynomials. https://arxiv.org/abs/1804.09875

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