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arXiv · 2202.06792

Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three

Yulia Karpeshina·Seonguk Kim·Roman Shterenberg
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Abstract

Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive "non-resonant" set ${\mathcal G} \subset \mathbb{R}^3$ such that for every $\vec k\in \mathcal G$ there is a solution asymptotically close to a plane wave $Ae^{i\langle{ \vec{k}, \vec{x} }\rangle}$ as $|\vec k|\to \infty $, given $A$ is sufficiently small.

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Yulia Karpeshina, Seonguk Kim, Roman Shterenberg. 2022-02-14. Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Three. https://arxiv.org/abs/2202.06792

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