NONLINEAR-THEORY OF OSCILLATING, DECAYING, AND COLLAPSING SOLITONS INTHE GENERALIZED NONLINEAR SCHRODINGER-EQUATION

A nonlinear theory describing the long-term dynamics of unstable solit ons in the generalized nonlinear Schrodinger (NLS) equation is propose d. An analytical model for the instability-induced evolution of the so liton parameters is derived in the framework of the perturbation theor y, which is valid near the threshold of the soliton instability. As a particular example, we analyze solitons in the NLS-type equation with two power-law nonlinearities. For weakly subcritical perturbations, th e analytical model reduces to a second-order equation with quadratic n onlinearity that can describe, depending on the initial conditions and the model parameters, three possible scenarios of the longterm solito n evolution: (i) periodic oscillations of the soliton amplitude near a stable state, (ii) soliton decay into dispersive waves, and (iii) sol iton collapse. We also present the results of numerical simulations th at confirm excellently the predictions of our analytical theory.