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The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems (1999)

Mallet-Paret, John

Springer

Journal of dynamics and differential equations 11 (1999), S. 49-127

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ISSN: 1572-9222

Keywords: Traveling waves ; spatially discrete systems ; lattice differential equations ; continuation methods ; heteroclinic orbits ; Lin's method ; Mel'nikov method

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1021841618074

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