On traveling wave solutions of nonlinear diffusion equations

  • Charles C. Conley
III. Nonlinear Differential Equations
Part of the Lecture Notes in Physics book series (LNP, volume 38)


An existence proof for periodic traveling wave solutions of an equation of Nagumo is outlined. The proof begins with the analysis of a limiting case in which one set of dependent variables moves infinitely fast compared to the remainder. Singular “orbits” are defined for this limiting system and a perturbation argument using isolating blocks allows one to find actual solutions.


Periodic Orbit Phase Portrait Travel Wave Solution Unstable Manifold Homoclinic Orbit 
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  1. [1]
    Conley, C., Hyperbolic sets and the shift automorphism, in this volume.Google Scholar
  2. [2]
    Carpenter, G., Thesis, University of Wisconsin, Madison.Google Scholar
  3. [3]
    Hastings, S., On traveling wave solutions of the Hodgkin-Huxley equations, (to appear).Google Scholar
  4. [4]
    Hastings, S., The existence of periodic solutions to Nagumo's equation (to appear), Quarterly Jour. of Math., September.Google Scholar
  5. [5]
    Hastings, S., The existence of homoclinic orbits for Nagumo's equation, (to appear).Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Charles C. Conley
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadison

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