Least Energy Solitary Waves for a System of Nonlinear Schrodinger Equations in \rn

Boyan Sirakov (1)

1 MODAL'X - Modélisation aléatoire de Paris X

In this paper we consider systems of coupled Schrödinger equations which appear in nonlinear optics. The problem has been considered mostly in the one-dimensional case. Here we make a rigorous study of the existence of least energy standing waves (solitons) in higher dimensions. We give : conditions on the parameters of the system under which it possesses a solution with least energy among all multi-component solutions ; conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie.

Domaines: Equations aux dérivées partielles [math.AP]

Boyan Sirakov. Least Energy Solitary Waves for a System of Nonlinear Schrodinger Equations in \rn. Communications in Mathematical Physics, 2007, 271 (1), pp.199-221. ⟨hal-00079184⟩