Parametric resonance for solitons in the nonlinear Schrödinger equation model with time-dependent harmonic oscillator potential

The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schrödinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose–Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered.