Short envelope solitons (combined nonlinear equation)

Abstract

A unified description of both short (on the order of a few wavelengths) envelope solitons and video solitons (without high-frequency filling) in dispersive media of different nature is given within the framework of the general third-order nonlinear equation of nonlinear dispersion theory. This solution includes, as particular cases, the well-known envelope solitons of the nonlinear Schrodinger equation (NSE), a modified Hirota equation, a combined nonlinear equation at the zero-dispersion point (ZDP), and video solitons of a modified Korteweg-de Vries (KdV) equation. An explicit soliton solution for inhomogeneous media is found within the framework of the third-order nonlinear equation with a linear-profile potential. This solution can be reduced to the well-known Chen-soliton solution. The examples of short intense solitons of electromagnetic and Langmuir waves in an isotropic plasma and of optical solitons in cubic nonlinear optical media are considered. In an isotropic plasma, the soliton velocity in a third-order approximation of nonlinear dispersion theory depends on the soliton amplitude. Short intense phase-modulated optical solitons are obtained for cubic nonlinear isotropic optical media. The length of these solitons is less than the length of NSE solitons. This increases the information capacity of fiberoptical lines of communication when a short base pulse is used.