Two-component nonlinear wave of the cubic Boussinesq equation

TL;DR

This paper derives explicit analytical two-component vector breather solutions for the cubic Boussinesq equation, revealing complex nonlinear wave behaviors with oscillations at combined frequencies and wave numbers.

Contribution

It introduces a generalized perturbation reduction method to obtain explicit two-component nonlinear wave solutions for the cubic Boussinesq equation.

Findings

Explicit analytical expressions for two-component nonlinear pulses

Solutions oscillate with sum and difference of frequencies and wave numbers

Enhanced understanding of complex wave interactions in nonlinear media

Abstract

In this work, we employ the generalized perturbation reduction method to find the two-component vector breather solution of the cubic Boussinesq equation $U_{tt} - C U_{zz} - D U_{zzzz}+G (U^{3})_{zz}=0$. 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 obtained.