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Solitary Waves for Linearly Coupled Nonlinear Schrödinger Equations with Inhomogeneous Coefficients

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Abstract

Motivated by the study of matter waves in Bose–Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrödinger equations with inhomogeneous parameters, including a linear coupling. For that system, we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnoselskii fixed point theorem together with a suitable compactness criterion.

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Authors and Affiliations

  1. Departamento de Matemáticas, E.T.S. de Ingenieros Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería (IMACI), Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain

    Juan Belmonte-Beitia & Víctor M. Pérez-García

  2. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva s/n, 18071, Granada, Spain

    Pedro J. Torres

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  1. Juan Belmonte-Beitia
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  2. Víctor M. Pérez-García
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  3. Pedro J. Torres
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Correspondence to Juan Belmonte-Beitia.

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Communicated by B. Eckhardt.

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Belmonte-Beitia, J., Pérez-García, V.M. & Torres, P.J. Solitary Waves for Linearly Coupled Nonlinear Schrödinger Equations with Inhomogeneous Coefficients. J Nonlinear Sci 19, 437–451 (2009). https://doi.org/10.1007/s00332-008-9037-7

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  • DOI: https://doi.org/10.1007/s00332-008-9037-7

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