Bifurcation Analysis of Reaction-Diffusion Equations. VI. Multiply Periodic Travelling Waves

The bifurcation of periodic travelling-wave solutions of a system of reaction-diffusion equations from a trivial solution is studied. We allow general periodicity conditions and show that the resulting bifurcation is characterized by the wave vector ${\bf k}$ and a wave speed c. Criteria for the global branching of such solutions are described and the results are applied to the Brusselator.