SELF-SIMILAR SOLUTIONS FOR A COUPLED SYSTEM OF NONLINEAR SCHRODINGER-EQUATIONS

This work is devoted to the study of self-similar solutions of the (2 + 1)-dimensional coupled nonlinear Schrodinger equations [GRAPHICS] where psi(1) and psi(2) are complex functions, h is a non-vanishing real parameter, eta = +/- 1 and epsilon = +/- 1. We give the point-symmetry properties of the model and calculate generic (2 + 1)-dimensional symmetry reductions. Some exact and approximate solutions are obtained. In particular, we use a variational approach to determine and classify a set of physically relevant localized non-singular self-similar solutions.