Two-component vector breather solution of the modified BBM equation

TL;DR

This paper derives explicit two-component vector breather solutions for the modified BBM equation using a generalized perturbation reduction method, transforming it into coupled nonlinear Schrödinger equations.

Contribution

It introduces a novel analytical approach to obtain explicit vector breather solutions for the modified BBM equation.

Findings

Explicit analytical expressions for vector breather solutions.

Breathers oscillate with sum and difference of frequencies and wavenumbers.

Solution method transforms the equation into coupled nonlinear Schrödinger equations.

Abstract

This is a continuation of Ref.[1](arXiv:nlin.PS/2001.07758v1). In the present paper, we consider the solution to the modified Benjamin-Bona-Mahony equation $u_{ t} + C u_{z} + \beta u_{zzt} + a u^{2} u_{z}=0$ using the generalized perturbation reduction method. The equation is transformed to the coupled nonlinear Schr\"odinger equations for auxiliary functions. Explicit analytical expression for the shape and parameters of the two-component vector breather oscillating with the sum and difference of frequencies and wavenumbers are obtained.