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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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