Lashkin V. Stable nonlinear coherent structures in dispersive media

Nonlinear coherent structures in media with dispersion and nonlinearity are investigated. Soliton perturbation theory based on the inverse scattering transform approach is developed for the physical tasks in models of the defocusing nonlinear Schrodinger equation, derivative nonlinear Schrodinger equation and modified nonlinear Schrodinger equation. Onedimensional and multidimensional soliton and vortex structures at the upper hybrid, ion cyclotron, drift branches of plasma oscillations, in plasma with an electron beam, in Bose-Einstein condensates are found. Stability analysis of these structures is performed. Azimuthon structures and their stability conditions are found. Vector states soliton-azimuthon and azimuthon-azimuthon are studied.