Traveling waves in coupled reaction-diffusion models with degenerate sources

Document Type

Article

Publication Date

1-1-2006

Abstract

We consider a general system of coupled nonlinear diffusion equations that are characterized by having degenerate source terms and thereby not having isolated rest states. Using a general form of physically relevant source terms, we derive conditions that are required to trigger traveling waves when a stable uniform steady-state solution is perturbed by a highly localized disturbance. We show that the degeneracy in the source terms implies that traveling waves have a number of surprising properties that are not present for systems with nondegenerate source terms. We also show that such systems can lead to a pair of waves that initially propagate outwards from the disturbance, slow down, and reverse direction before ultimately colliding and annihilating each other. © 2006 The American Physical Society.

Identifier

34548335613 (Scopus)

Publication Title

Physical Review E Statistical Nonlinear and Soft Matter Physics

External Full Text Location

https://doi.org/10.1103/PhysRevE.74.021909

e-ISSN

15502376

ISSN

15393755

PubMed ID

17025474

Issue

2

Volume

74

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