Title :

Logarithmic Gross-Pitaevskii equation

Author(s) :

Carles, Rémi [Auteur]
Institut de Recherche Mathématique de Rennes [IRMAR]
Ferriere, Guillaume [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Institut de Recherche Mathématique Avancée [IRMA]

Journal title :

Communications in Partial Differential Equations

Pages :

88-120

Publisher :

Taylor & Francis

Publication date :

2024-02-06

ISSN :

0360-5302

English keyword(s) :

Gross-Pitaevskii
logarithmic nonlinearity
Cauchy problem
solitary wave
traveling wave

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation

Comment :

31 pages. Accepted in Communications in Partial Differential Equations and published online on 29 Dec 2023.

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL