Two-component nonlinear wave of the Born-Infeld equation

TL;DR

This paper derives a two-component vector breather solution for the Born-Infeld equation using a perturbative reduction method, revealing oscillations with combined frequencies and wave numbers.

Contribution

It introduces a novel two-component nonlinear wave solution for the Born-Infeld equation using the generalized perturbative reduction method.

Findings

Solution oscillates with sum and difference of frequencies and wave numbers

Demonstrates complex wave interactions in nonlinear Born-Infeld dynamics

Provides analytical form of two-component vector breather

Abstract

The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - \sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown that the solution of the two-component nonlinear wave oscillates with the sum and difference of frequencies and wave numbers.