Stable small-amplitude solutions in reaction-diffusion systems
Bifurcation and perturbation techniques are used to construct smallamplitude periodic wave-trains for general systems of reaction and diffusion. All solutions are characterized by the amplitude a and the wavenumber k. For scalar diffusion, k ~ a, while for certain types of nonscalar diffusion, k is bounded away from zero as a\0. For certain ranges of a and k, linear stability of waves is demonstrated.