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arXiv · 1911.03944

Coercivity for travelling waves in the Gross-Pitaevskii equation in $\mathbb{R}^2$ for small speed

David Chiron·Eliot Pacherie
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Abstract

In the previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space. In particular, our result proves the non degeneracy of these travelling waves, which is a key step in the classification of these waves and for the construction of multi-travelling waves.

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David Chiron, Eliot Pacherie. 2019-11-10. Coercivity for travelling waves in the Gross-Pitaevskii equation in $\mathbb{R}^2$ for small speed. https://doi.org/10.5565/publmat6712307

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