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

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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.

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  1. Modalx, Ufr Segmi, Université Paris 10, 92001, Nanterre Cedex, France

    Boyan Sirakov

  2. Cams, Ehess, 54 bd Raspail, 75270, Paris Cedex 06, France

    Boyan Sirakov

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  1. Boyan Sirakov
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Correspondence to Boyan Sirakov.

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Communicated by P. Constantin

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Sirakov, B. Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in \({\mathbb{R}^n}\) . Commun. Math. Phys. 271, 199–221 (2007). https://doi.org/10.1007/s00220-006-0179-x

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