Abstract
A new, geometric proof of a theorem of Fife, Palusinski, and Su on electrophoretic traveling waves is presented. The proof is based upon the perturbation theory for invariant manifolds due to Fenichel. The results proved here reproduce the existence, uniqueness, and asymptotic approximation theorem proved by Fifeet al. The proof given here is substantially simpler, and in addition, it provides additional insight into the geometric structure of the phase space of the traveling wave equations for this system.
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References
Fenichel, N. (1971). Persistence and smoothness of invariant manifolds for flows.Indiana Univ. Math. J. 21, 193–226.
Fife, P. C., Palusinski, O. A., and Su, Y. (1988). Electrophoretic travelling waves.Transactions A.M.S. 310, 759–780.
Wiggins, S. (1988).Global Bifurcations and Chaos. Springer-Verlag.
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Gardner, R.A. An invariant-manifold analysis of electrophoretic traveling waves. J Dyn Diff Equat 5, 599–606 (1993). https://doi.org/10.1007/BF01049140
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DOI: https://doi.org/10.1007/BF01049140