D.E. Pelinovsky
Radiative effects to the adiabatic dynamics of envelope-wave solitons
Physica D 119, 301-320 (1998)
Abstract:
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 at the background
of a stable soliton near the instability threshold.
Keywords:
NONLINEAR SCHRODINGER-EQUATION, SELF-FOCUSING SINGULARITY,
SIMILARITY STRUCTURE, CRITICAL DIMENSION, OPTICAL BEAMS,
COLLAPSE, DISPERSION