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Zbl 0921.34046
Mallet-Paret, John
The global structure of traveling waves in spatially discrete dynamical systems.
(English)
[J] J. Dyn. Differ. Equations 11, No.1, 49-127 (1999). ISSN 1040-7294; ISSN 1572-9222/e

Summary: The author obtains the existence of travelling wave solutions for a class of spatially discrete systems, namely, lattice differential equations. Uniqueness of the wave speed $c$, and uniqueness of the solution with $c\ne 0$, are shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where $c\ne 0$. Convergence results for solutions are obtained at the singular perturbation limit $c\to 0$.
MSC 2000:
*37-99 Dynamic systems and ergodic theory
34A35 ODE of infinite order
34C37 Homoclinic and heteroclinic solutions of ODE

Keywords: uniqueness; existence; travelling wave solutions; spatially discrete systems; lattice differential equations

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