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Exact travelling wave solutions of an “integrable” discrete reaction-diffusion equation

✍ Scribed by P.C. Bressloff; G. Rowlands

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
774 KB
Volume
106
Category
Article
ISSN
0167-2789

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✦ Synopsis

We construct exact travelling wave solutions of a discrete reaction~liffusion equation describing a system of coupled bistable elements. The form of the bistable potential is chosen such that in a moving frame the wavefonn satisfies an integrable discrete equation that can be solved explicitly. We analyse the linear stability of the wave and study wave propagation failure in the weak coupling limit.

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Travelling wave solutions of a fourth-order semilinear diffusion equation
✍ M.E. Akveld; J. Hulshof 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 360 KB

We establish existence of travelling waves for a fourth-order semilinear diffusion equation and examine the dependence of the wave speed on the parameter. Keywords--Singular perturbation, Travelling waves, Rate of change of wave speed.