Nonlinear theory of oscillating, decaying, and collapsing solitons in the generalized nonlinear Schrödinger equation

A nonlinear theory describing the long-term dynamics of unstable solitons in the generalized nonlinear Schrödinger (NLS) equation is proposed. An analytical model for the instability-induced evolution of the soliton parameters is derived in the framework of the perturbation theory, 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 …