Two-Component Vector Breather

Abstract

A two-component solution of the modified Benjamin-Bona-Mahoney equation is considered. Using a generalized perturbative reduction method, the equation is transformed to coupled nonlinear Schrödinger equations for auxiliary functions. An explicit analytical expression is obtained for the shape and parameters of a two-component vector breather, the components of which oscillate at the sum and difference frequencies and wavenumbers.

Two-component breather solution of the nonlinear Klein-Gordon equation

“…In order to consider the two-component vector breather solution of the Eq. ( 3), we use the generalized perturbative reduction method [7][8][9][10][11][12][13][14][15][16][17][18] which makes it possible to transform the nonlinear Klein-Gordon equation for the functions ûl to the coupled nonlinear Schrödinger equations for auxiliary functions. As a result, we obtain a two-component nonlinear pulse oscillating with the difference and sum of the frequencies and wave numbers.…”

“…The purpose of the present work is to consider the two-component vector breather (0π pulse) solution of the nonlinear Klein-Gordon equation (3) using the generalized perturbative reduction method [7][8][9][10][11][12][13][14][15][16][17][18] and obtain twocomponent vector breather solution in the same conditions Eq. ( 5) as for the Bloch-Maxwell equation.…”

The Two-Component Breather Solution of the Hirota Equation

“…Although the vector 0π pulse of self-induced transparency, which is a special type of two-breather molecule, was first noticed for optical nonlinear waves, later, using the generalized perturbative reduction method, the same two-breather molecules were discovered for waves of a different nature described by other nonlinear partial differential equations, such as are the Boussinesq-type equation, the Benjamin-Bona-Mahony equation, and the Hirota equation [7,9,[35][36][37].…”