Autoresonance excitation of a soliton of the nonlinear Schrödinger equation (Q2447024)

The paper is dealing with the nonlinear Schrödinger equation, which contains a linear dissipative term and a driving term. The latter one depends on the wave function, time, and the spatial coordinate. The autoresonance effect implies that a soliton, which is supported, in the presence of the linear dissipation, by the resonant driving term, is able to follow an adiabatically slow variation of the frequency and other parameters of the drive. In this work, this effect is analyzed in detail by means of the perturbation theory for solitons , which reduces the problem to the study of the autoresonance in an effective mechanical system for parameters of the soliton.