Front propagation under periodic forcing in reaction-diffusion systems

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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\xi_0$</EquationSource> </InlineEquation>) 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. Copyright Springer-Verlag Berlin/Heidelberg 2003