Communications in Mathematical Physics

, Volume 271, Issue 1, pp 199–221

Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in \({\mathbb{R}^n}\)

Article

DOI: 10.1007/s00220-006-0179-x

Cite this article as:
Sirakov, B. Commun. Math. Phys. (2007) 271: 199. doi:10.1007/s00220-006-0179-x

Abstract

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.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Modalx, Ufr SegmiUniversité Paris 10Nanterre CedexFrance
  2. 2.Cams, EhessParis Cedex 06France