Solitons and solitonic vortices in a strip

Amandine Aftalion (1) , Etienne Sandier

1 CAMS - Centre d'Analyse et de Mathématique sociales

We study the ground state of the Gross Pitaveskii energy in a strip, with a phase imprinting condition, motivated by recent experiments on matter waves solitons. We prove that when the width of the strip is small, the ground state is a one dimensional soliton. On the other hand, when the width is large, the ground state is a solitonic vortex. We provide an explicit expression for the limiting phase of the solitonic vortex as the size of the strip is large: it has the same behaviour as the soliton in the infinite direction and decays exponentially due to the geometry of the strip, instead of algebraically as vortices in the whole space.

Mots clés: Gross Pitaevskii energy; vortex; soliton

Domaines: Equations aux dérivées partielles [math.AP]; Matière Condensée [cond-mat]

Amandine Aftalion, Etienne Sandier. Solitons and solitonic vortices in a strip. Nonlinear Analysis: Theory, Methods and Applications, 2023, 228, pp.113184. ⟨10.1016/j.na.2022.113184⟩. ⟨hal-03666286v3⟩