Smooth branch of travelling waves for the Gross-Pitaevskii equation in R2 for small speed

• David Chiron ^[1] ; Eliot Pacherie ^[1]
  1. [1] Université de Nice, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 4, 2021, págs. 1937-2038
• Idioma: inglés
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• Resumen

  • We construct a smooth branch of travelling wave solutions for the 2- dimensional Gross-Pitaevskii equations for small speed. These travelling waves exhibit two vortices far away from each other. We also compute the leading order term of the derivatives with respect to the speed. We construct these solutions by an implicit function type argument