On the existence of pulses in reaction-diffusion-equations

DOI10.1007/BF03323079zbMath0762.35050MaRDI QIDQ1193221

Klaus R. Schneider

Publication date: 27 September 1992

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

hyperbolic equilibriumtheory of invariant manifolds

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Singular perturbations of ordinary differential equations (34D15) Invariant manifolds for ordinary differential equations (34C45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Invariant manifolds of singularly perturbed ordinary differential equations
• Isolating blocks and symbolic dynamics
• A geometric approach to singular perturbation problems with applications to nerve impulse equations
• On travelling wave solutions of the Hodgkin-Huxley equations
• Exponential dichotomies and transversal homoclinic points
• Isolated invariant sets in compact metric spaaces
• The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
• ON THE EXISTENCE OF HOMOCLINIC AND PERIODIC ORBITS FOR THE FITZHUGH-NAGUMO EQUATIONS
• Perturbation analysis of an approximation to the Hodgkin-Huxley theory
• Mathematical Aspects of Hodgkin-Huxley Neural Theory
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