Radiative effects to the adiabatic dynamics of envelope-wave solitons

A general asymptotic method for analysis of radiative effects to the adiabatic dynamics of envelope-wave solitons is presented in the form of a modified soliton perturbation technique involving three asymptotic scales. This method is applied to a generalized NLS equation for description of both the instability-induced soliton dynamics near the instability threshold and exponentially weak radiative effects. The results are obtained for two particular problems: (i) a new (revised) derivation of a double-logarithmic scaling law of singularity formation at the critical soliton collapse and (ii) calculation of an inverse squared logarithmic decay rate of an amplitude of internal low-frequency oscillations excited as the background of a stable soliton near the instability threshold.