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Journal of Dynamics and Differential Equations

, Volume 11, Issue 1, pp 49–127 | Cite as

The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems

  • John Mallet-Paret
Article

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.

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

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Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • John Mallet-Paret
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidence

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