Abstract
We obtain existence of traveling 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≠0, are also shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where c≠0. Convergence results for solutions are obtained at the singular perturbation limit c → 0.
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Mallet-Paret, J. The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems. Journal of Dynamics and Differential Equations 11, 49–127 (1999). https://doi.org/10.1023/A:1021841618074
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DOI: https://doi.org/10.1023/A:1021841618074