Exact analytical solutions of the reaction-diffusion equations with spatial inhomogeneous reaction and diffusion coefficients are found. It is shown that the space-oscillating approximate solution of a traveling wave type [P.K. Brazhnik, J.J. Tyson, SIAM J. Appl. Math. <Emphasis Type="Bold">60, 371 (1999)] is the...</emphasis>

Front solutions in a reaction–diffusion equations with cutoff are obtained analytically using piecewise linear approximations of the reaction term. The piecewise emulation allows us to study analytically the effect of the cutoff for fronts propagating into metastable and unstable states. A...

The front dynamics in reaction–diffusion equations with a piecewise linear reaction term is studied. A transition from pushed-to-pulled fronts when they propagate into the unstable state is found using a variational principle. This transition occurs for a critical value of the discontinuity...

We consider a two-component system of reaction-diffusion equations with a small cutoff in the reaction term. A semi-analytical solution of fronts and how the front velocities vary with the parameters are given for the case when the system has a piecewise linear nonlinearity. We find the...

A stability analysis is performed analytically for the tristable reaction-diffusion equation, in which a quintic reaction term is approximated by a piecewise linear function. We obtain growth rate equations for two basic types of propagating fronts, monotonous and nonmonotonous ones. Their...

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....