Fisher–Kolmogorov equation

Ronald Fisher

Andrey Kolmogorov

Fisher–Kolmogorov equation named after Ronald Fisher and Andrey Kolmogorov, the former contributing Fisher's equation and the latter also publishing in 1937,^[1] is a nonlinear reaction-diffusion equation of the form^[2][3]

$\frac{\partial u}{\partial t}-\frac{\partial^2 u}{\partial x^2}=\frac{\alpha}{k}u(1-u^q).\,$

The Fisher–Kolmogorov equation like many reaction-diffusion has an important application in biology as well as in chemistry.

References

1. Fisher 2
2. Graham W. Griffiths, William E. Schiesser, Traveling Wave Analysis of Partial Differential Equations, Chapter 8 "Fisher–Kolmogorov Equation", pp 135–146 Academy Press
3. G. Adomian, "Fisher–Kolmogorov equation", Applied Mathematics Letters, volume 8, issue 2, March 1995, pages 51–52

Further reading

1. Graham W. Griffiths William E. Shiesser Traveling Wave Analysis of Partial Differential Equations, Academic Press
2. Richard H. Enns George C. McCGuire, Nonlinear Physics, Birkhauser, 1997
3. Inna Shingareva, Carlos Lizárraga-Celaya, Solving Nonlinear Partial Differential Equations with Maple, Springer.
4. Eryk Infeld and George Rowlands, Nonlinear Waves, Solitons and Chaos, Cambridge 2000
5. Saber Elaydi, An Introduction to Difference Equations, Springer 2000
6. Dongming Wang, Elimination Practice, Imperial College Press 2004
7. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis, Springer, 1998 ISBN 9780387983004
8. George Articolo, Partial Differential Equations and Boundary Value Problems with Maple V, Academic Press 1998 ISBN 9780120644759