Article

Communications in Mathematical Physics

, Volume 271, Issue 1, pp 199-221

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

  • Boyan SirakovAffiliated withModalx, Ufr Segmi, Université Paris 10Cams, Ehess Email author 

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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.