Stable small-amplitude solutions in reaction-diffusion systems
- 1 January 1981
- journal article
- Published by American Mathematical Society (AMS) in Quarterly of Applied Mathematics
- Vol. 39 (1) , 61-86
- https://doi.org/10.1090/qam/613952
Abstract
Bifurcation and perturbation techniques are used to construct small-amplitude periodic wave-trains for general systems of reaction and diffusion. All solutions are characterized by the amplitude a a and the wavenumber k k . For scalar diffusion, k ∼ a k \sim a , while for certain types of nonscalar diffusion, k k is bounded away from zero as a ↘ 0 a \searrow 0 . For certain ranges of a a and k k , linear stability of waves is demonstrated.Keywords
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