Two-component nonlinear wave solutions of the sixth-order generalised Boussinesq-type equations

Abstract

Two different versions of cubic sixth-order generalised Boussinesq-type wave equations are considered in this study. A generalised perturbation reduction method is used to solve these equations, which allows the reduction of considered equations to coupled nonlinear Schrodinger equations. Two-component nonlinear wave solutions are obtained. The profiles and parameters of these solutions for both nonlinear equations are presented and compared. These solutions coincide with the vector 0 πpulse of self-induced transparency, which was previously studied in several known nonlinear wave equations.