Two-component nonlinear wave of the cubic Boussinesq-type equation

The general form of the cubic Boussinesq-type equation is considered. In special cases, this reduced to three different versions Boussinesq equations and also generalized modified equation. Using slowly varying envelope approximation perturbation reduction method transformed coupled nonlinear Schrodinger two-component solitary wave solution obtained. Explicit analytical expressions for shape parameters pulse oscillating with sum difference frequencies numbers are presented. It shown that obtained coincides vector $0\pi$ self-induced transparency.