Global Bifurcation in Symmetric Systems of Nonlinear Wave Equations

TL;DR

This paper employs equivariant degree theory to prove a global bifurcation result for non-stationary solutions in symmetric nonlinear wave systems with delays and damping, exemplified by coupled vibrating strings.

Contribution

It introduces a novel application of equivariant degree theory to establish global bifurcation in symmetric hyperbolic wave equations with delays and damping.

Findings

Existence of non-stationary solution branches established

Application to coupled vibrating strings demonstrates practical relevance

Global bifurcation results extend understanding of symmetric nonlinear wave systems

Abstract

In this paper, we use the equivariant degree theory to establish a global bifurcation result for the existence of non-stationary branches of solutions to a nonlinear, two-parameter family of hyperbolic wave equations with local delay and non-trivial damping. As a motivating example, we consider an application of our result to a system of $N$ identical vibrating strings with dihedral coupling relations.