English

Index theory for traveling waves in reaction diffusion systems with skew gradient structure

Analysis of PDEs 2020-10-13 v2 Dynamical Systems

Abstract

A unified geometric approach for the stability analysis of traveling pulse solutions for reaction-diffusion equations with skew-gradient structure has been established in a previous paper [9], but essentially no results have been found in the case of traveling front solutions. In this work, we will bridge this gap. For such cases, a Maslov index of the traveling wave is well-defined, and we will show how it can be used to provide the spectral information of the waves. As an application, we use the same index providing the exact number of unstable eigenvalues of the traveling front solutions of FitzHugh-Nagumo equation.

Keywords

Cite

@article{arxiv.2010.03126,
  title  = {Index theory for traveling waves in reaction diffusion systems with skew gradient structure},
  author = {Qin Xing},
  journal= {arXiv preprint arXiv:2010.03126},
  year   = {2020}
}

Comments

15 pages

R2 v1 2026-06-23T19:06:41.334Z