Problem of Stability of Solutions of the Generalized Nonlinear Schrödinger Equation in Nonuniform and Nonstationary Media

Abstract

On the basis of the analytical and numerical approaches the stability and dynamics of interaction of the multidimensional soliton-like solutions of the generalized nonlinear Schrödinger equation, which describes the waves in a plasma, fiber and planar optical waveguides, taking into account inhomogeneity and nonstationarity of propagation medium, is studied. The sufficient conditions of stability of the 2-dimensional and 3-dimensional solutions are obtained, and it is shown that even in the simplest 1-dimensional case the GNLS equation can have stable and quasi-stable solutions of the soliton and breather types and also unstable solutions which disperses with time. Obtained results can be useful in numerous applications in plasma physics, nonlinear optics and in many other fields of physics.