Abstract
In a previous paper, we constructed a smooth branch of travelling waves for the -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 nondegeneracy of these travelling waves, which is a key step in their classification and for the construction of multi-travelling waves.
Citation
David Chiron. Eliot Pacherie. "COERCIVITY FOR TRAVELLING WAVES IN THE GROSS–PITAEVSKII EQUATION IN FOR SMALL SPEED." Publ. Mat. 67 (1) 277 - 410, 2023. https://doi.org/10.5565/PUBLMAT6712307
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