Construction of exact travelling waves for the Benjamin-Bona-Mahony equation on networks

TL;DR

This paper constructs explicit travelling wave solutions for the Benjamin-Bona-Mahony equation on networks, establishing conditions on coefficients and network geometry for their existence, advancing understanding of wave propagation in complex structures.

Contribution

It provides a novel explicit wave construction on the real line and derives conditions for the existence of travelling waves on networks, linking wave solutions to network geometry and coefficients.

Findings

Explicit travelling wave constructed on $\\mathbb{R}$

Conditions on coefficients for wave existence on networks

Wave existence depends on network geometry

Abstract

We are interested in the existence of travelling waves for the Benjamin-Bona-Mahony equation on a network. First we construct an explicit wave, defined in $\mathbb{R}$. Then, we use this wave to derive some conditions on the coefficients appearing in the equations and on the geometry of the network to ensure the existence of travelling waves on the network.