Semiclassical nonlinear Schrödinger equations with potential and focusing initial data

Rémi Carles (1, 2) , Luc Miller (3, 4)

1 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 CMLS - Centre de Mathématiques Laurent Schwartz
4 MODAL'X - Modélisation aléatoire de Paris X

We study the asymptotic behaviour of solutions to semi-classical nonlinear Schrödinger equations with a potential, for concentrating and oscillating initial data, when the nonlinearity is repulsive and the potential is a polynomial of degree at most two. We describe the separate roles of the nonlinearity and of the potential, with tools which seem to be specific to the class of potentials that we consider. We also discuss the case of more general subquadratic potentials.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Rémi Carles, Luc Miller. Semiclassical nonlinear Schrödinger equations with potential and focusing initial data. Osaka J. Math., 2004, 41, pp.693-725. ⟨hal-00004969⟩