Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients
J. Belmonte-Beitia, V. M. Perez-Garcia, P. J. Torres
Journal of Nonlinear Science, 19, 437-451 (2009).
Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger 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.