Two-component nonlinear wave of the NLS equation

Abstract

Using the generalized perturbation reduction method the scalar nonlinear Schrödinger equation is transformed to the coupled nonlinear Schrödinger equations for auxiliary functions. A solution in the form of a two-component vector nonlinear pulse is obtained. The components of the pulse oscillate with the sum and difference of the frequencies and wave numbers. Explicit analytical expressions for the shape and parameters of the two-component nonlinear pulse are presented.