Communications in Mathematical Physics

, Volume 271, Issue 1, pp 199–221 | Cite as

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

  • Boyan SirakovEmail author


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.


Soliton Sobolev Inequality Energy Solution Unique Positive Solution Nonlinear Elliptic System 
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© Springer-Verlag 2007

Authors and Affiliations

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

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