Solitary waves for linearly coupled nonlinear Schrodinger equations with   inhomogeneous coefficients
  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. 
Juan Belmonte Beitia, Victor M. Perez Garcia and Pedro J. Torres