Extended Parametric Resonances in Nonlinear Schrödinger Systems

Abstract

We study an example of exact parametric resonance in an extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the same way. The results have applicability in recent experiments in Bose-Einstein condensation and to classical problems in nonlinear optics.