Perturbation theory and soliton dynamics
K.A. Gorshkov, L.A. Ostrovsky, Yu.A. Stepanyants
Institute of Applied Physics, Nizhni Novgorod, Russia
A new life of a soliton as a particle-like wave has started from treating of the integrable equations by new exact analytical methods as well as by the computing (both ways were open with direct participation of M. Kruskal). Later, perturbation theories were developed permitting one to describe soliton dynamics in the presence of small perturbations, both in integrable and non-integrable systems. Here we give a brief review of soliton dynamics theory based on the ''direct'' perturbation method for solitons, in application to different classes of equations. In particular, we discuss: 1. Ensembles of interacting solitons: bound states, soliton lattices, multisolitons, etc. 2. Interaction of solitons with a long wave in a dissipative medium resulting in a ''parametric'' amplification and generation of solitons and their groups. 3. ''Quasisolitons'' in rotating fluids where the exact solitary solutions are impossible but a radiating soliton may exist for a finite period of time.