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