Self-similar solutions for a coupled system of nonlinear Schrodinger equations

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Abstract
This work is devoted to the study of self-similar solutions of the (2+1)-dimensional coupled nonlinear Schrodinger equations which occur in nonlinear optics-1 psi (1)Z+ psi (1)xx+ psi (1)yy+ eta ( mod psi (1) to 2+(1+h) mod psi (2) mod 2) psi (1)=0 and square root -1 psi (2)+ psi (2)xx+ psi (2)yy+ eta ( mod psi (2) mod 2+(1+h) mod psi (1)) psi (2)=0 where psi (1) and psi (2) are complex functions, h is a non-vanishing real parameter, eta =+or-1 and in =+or-1. The authors 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, they use a variational approach to determine and classify a set of physically relevant localized nonsingular self-similar solutions.