Coercivity for travelling waves in the Gross-Pitaevskii equation in R2 for small speed
Chiron, David (Université de Nice-Sophia Antipolis. Laboratoire de Mathématiques J. A. Dieudonné)
Pacherie, Eliot 
(Université de Nice-Sophia Antipolis. Laboratoire de Mathématiques J. A. Dieudonné)
| Fecha: |
2023 |
| Resumen: |
In a 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 nondegeneracy of these travelling waves, which is a key step in their classification and for the construction of multitravelling waves. |
| Derechos: |
Tots els drets reservats.  |
| Lengua: |
Anglès |
| Documento: |
Article ; Versió publicada |
| Materia: |
Travelling waves ;
Coercivity ;
Local uniqueness |
| Publicado en: |
Publicacions matemàtiques, Vol. 67 Núm. 1 (2023) , p. 277-410 (Articles) , ISSN 2014-4350 |
Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/412704
DOI: 10.5565/PUBLMAT6712307
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