Traveling waves in coupled reaction-diffusion models with degenerate sources

Jonathan J. Wylie, Robert M. Miura
2006 Physical Review E  
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
more » ... f surprising properties that are not present for systems with non-degenerate 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. PACS number(s): 87.15.Vv, 87.18.Pj
doi:10.1103/physreve.74.021909 pmid:17025474 fatcat:o3cjjnufprdt3efkgbrvrjxf6q