Regensburg 2004 – scientific programme
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.29: Poster
Thursday, March 11, 2004, 16:00–18:00, Poster D
Traveling waves in a reaction-diffusion system under periodic forcing — •E. P. Zemskov1, K. Kassner1, and S. C. Mueller2 — 1Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg — 2Institut fuer Experimentelle Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg
A one-component reaction-diffusion system under external force is considered. The simplest case of a periodic forcing of cosine type is chosen. Exact analytical solutions for the two basic types of traveling waves, fronts and pulses, are obtained in the case of a piecewise linear approximation of the non-linear reaction term. Velocity equations are derived from the matching conditions. Restrictions that arise during the derivation of the pulse velocity equations are stated and their origin is explained. It is found that in the presence of nonconstant forcing there exists a set of wave solutions with different phases (matching point coordinates). The general characteristic feature is that nonmoving waves become movable under forcing. However, for specific choices of forcing parameters, the traveling waves are pinned (stopped). The pinning conditions are obtained and discussed. It is found that in the case of periodic forcing there are infinite sets of the pinning positions. The phase portraits of specific types of solutions are shown and briefly discussed.
References
E. P. Zemskov, K. Kassner, S. C. Mueller, Eur. Phys. J. B 34, 285 (2003).