Coercivity for travelling waves in the Gross-Pitaevskii equation in R 2 for small speed

David Chiron (1) , Eliot Pacherie

1 LJAD - Laboratoire Jean Alexandre Dieudonné

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 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.

Mots clés: MSC classification (2010): 35C07; 35Q55; 35A02; 35B35 Travelling waves; Coercivity; Local uniqueness

Domaines: Equations aux dérivées partielles [math.AP]

David Chiron, Eliot Pacherie. Coercivity for travelling waves in the Gross-Pitaevskii equation in R 2 for small speed. Publicacions Matemàtiques, In press. ⟨hal-03326269⟩