Capture and confinement of solitons in nonlinear integrable systems

Abstract

The system describing the interaction of a long wave with a short wave packet on thex,y plane is considered. The solutions are found to describe a soliton that comes from infinity and then is captured into a conditionally periodical oscillatory regime. The solutions are also found that describe a soliton coming from infinity and then decaying into two solitons: one goes to infinity and the other is captured into a conditionally periodical oscillatory regime. The obtained results are relevant to some problems of hydrodynamics, plasma physics, solid state physics, etc.