https://doi.org/10.1140/epjb/e2003-00224-2
Front propagation under periodic forcing in reaction-diffusion systems
1
Institut für Theoretische Physik, Otto-von-Guericke-Universität, Universitätsplatz 2,
39106 Magdeburg, Germany
2
Institut für Experimentelle Physik, Otto-von-Guericke-Universität, Universitätsplatz 2,
39106 Magdeburg, Germany
Corresponding author: a zemskov@physik.uni-magdeburg.de
Received:
3
March
2003
Revised:
4
June
2003
Published online:
11
August
2003
One- and two-component bistable reaction-diffusion
systems under external force are considered. The simplest case of a
periodic forcing of cosine type is chosen. Exact analytical solutions
for the traveling fronts are obtained for a piecewise linear
approximation of the non-linear reaction term. Velocity equations are
derived from the matching conditions. It is found that in the presence
of forcing there exists a set of front solutions with different phases
(matching point coordinates 
) leading to velocity dependencies
on the wavenumber that are either monotonic or oscillating.
The general characteristic feature is that the nonmoving front becomes
movable under forcing. However, for a specific choice of wavenumber and
phase, there is a nonmoving front at any value of the forcing
amplitude. When the forcing amplitude is large enough, the velocity
bifurcates to form two counterpropagating fronts. The phase portraits
of specific types of solutions are shown and briefly discussed.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 47.20.Ma – Interfacial instability / 47.54.+r – Pattern selection; pattern formation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003
