Logarithmic Gross-Pitaevskii equation

Rémi Carles (1) , Guillaume Ferriere (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IRMA - Institut de Recherche Mathématique Avancée

We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which turns out to correspond to the energy space for the standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions. We then characterize the solitary and travelling waves in the one dimensional case.

Domaines: Equations aux dérivées partielles [math.AP]

Rémi Carles, Guillaume Ferriere. Logarithmic Gross-Pitaevskii equation. 2022. ⟨hal-03790977v1⟩