A Reverse Infinite-Period Bifurcation for the Nonlinear Schrodinger Equation in 2+1 Dimensions with a Parametric Excitation

Abstract

We consider the nonlinear Schrodinger equation in 2+1 dimensions and an external periodic excitation in parametric resonance with the frequency of a generic mode. Using an adequate perturbation method we get two coupled equations for the amplitude and phase. We show frequency-response curves and demonstrate the existence for the focusing case of a reverse infinite-period bifurcation when the parametric excitation increases its value. The same bifurcation is possible even in the defocusing case but for a different excitation amplitude value.