Huxley and Fisher equations for gene propagation: An exact solution

DOI10.1017/S1446181100007860zbMath1043.35041OpenAlexW2112877912MaRDI QIDQ3146189

G. R. Fulford, B. H. Bradshaw, Philip Broadbridge, Geoffrey K. Aldis

Publication date: 2002

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181100007860

zbMATH Keywords

reaction-diffusion equationsCubic source termsgene-transport equationsnon-uniform convection termzero gradient boundary condition

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Solutions to PDEs in closed form (35C05)

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Uses Software

• PDETWO

Cites Work

• A quasilinar heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures
• Explicit solutions of Fisher's equation for a special wave speed
• Symmetry reductions and exact solutions of a class of nonlinear heat equations
• New similarity reductions of the Boussinesq equation
• General Software for Two-Dimensional Nonlinear Partial Differential Equations
• Analytic solutions of the Nagumo equation
• Nonclassical symmetry reductions of the linear diffusion equation with a nonlinear source
• Modelling with Differential and Difference Equations