Solitary waves in excitable systems with cross-diffusion

DOI10.1098/rspa.2005.1529zbMath1370.35174OpenAlexW2119588843MaRDI QIDQ5428333

V. N. Biktashev, M. A. Tsyganov

Publication date: 21 November 2007

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2005.1529

zbMATH Keywords

predator-preynonlinear Schrödinger equationsolitonsFitzHugh-Nagumo systemautowavestwo-scale asymptotics

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Soliton equations (35Q51)

Related Items (7)

A PREDATOR–PREY INTERACTION MODEL WITH SELF- AND CROSS-DIFFUSION IN AQUATIC SYSTEMS ⋮ Solitary waves in the excitable Burridge-Knopoff model ⋮ Asymptotics of conduction velocity restitution in models of electrical excitation in the heart ⋮ EMERGENCE OF OSCILLATORY TURING PATTERNS INDUCED BY CROSS DIFFUSION IN A PREDATOR–PREY SYSTEM ⋮ Pattern selection in the 2D FitzHugh-Nagumo model ⋮ Nonlinear waves in a quintic FitzHugh–Nagumo model with cross diffusion: Fronts, pulses, and wave trains ⋮ Traveling Waves Impulses of FitzHugh Model with Diffusion and Cross-Diffusion

Cites Work

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• Front propagation and segregation in a reaction-diffusion model with cross-diffusion
• Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator--prey pursuit and evasion example
• A Modern Introduction to the Mathematical Theory of Water Waves
• Pursuit-evasion predator-prey waves in two spatial dimensions
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