Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Stable small-amplitude solutions in reaction-diffusion systems

Author: G. Bard Ermentrout
Journal: Quart. Appl. Math. 39 (1981), 61-86
MSC: Primary 35K55; Secondary 35B32, 80A30
DOI: https://doi.org/10.1090/qam/613952
MathSciNet review: 613952
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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$ and the wavenumber $ k$. For scalar diffusion, $ k \sim a$, while for certain types of nonscalar diffusion, $ k$ is bounded away from zero as $ a \searrow 0$. For certain ranges of $ a$ and $ k$, linear stability of waves is demonstrated.

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DOI: https://doi.org/10.1090/qam/613952
Article copyright: © Copyright 1981 American Mathematical Society

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