Abstract
In this work, we consider a Fisher and generalized Fisher equations with variable coefficients. Using truncated Painlevé expansions of these equations, we obtain exact solutions of these equations with a constraint on the coefficients a(t) and b(t).
Similar content being viewed by others
References
Ablowitz, M., Segur, H. Solitons and the inverse scattering transform. SIAM, Philadelphia, 1985
Ablowitz, M.J., Ramani, A., Segur, H. A connection between nonlinear evolution equations and ordinary differential equations of p-type I. J. Math. Phys., 21:715–721 (1980)
Cariello, F., Tabor, M. Similarity reductions from extended painlevé expansions for nonintegrable evolution equation. Physica D., 53:59–70 (1991)
Hong, W.P., Jung, Y.D. Auto-baclund transformation and analytic solutions for general variable coefficient kdv equation. Phys. Lett. A., 257:149–152 (1999)
Hong, W.P. Backlund transformation for a generalized burgers equation and solitonic solutions. Phys. Lett. A.,268:81–84 (2000)
Hutlsman, W.D., Halford, M.V. Exact solutions to kdv equations with variable coefficients and/or nonuniformities. Comp. Math. Applic., 29(1):39–47 (1995)
Kawahara, T., Tanaka, M. Interactions of traveling fronts:an exact solution of a nonlinear diffusion equation. Physics Letters., 97A(8):311–314 (1983)
Nirmala, N., Vedan, M.J., Baby, B.V. Auto-baclund transformation, lax pairs, and painlevé property of a variable coefficient korteweg-de vries equation with nonuniformities. J. Math. Phys., 27(11):2640–2643 (1986)
Steeb, W.H., Euler, N. Nonlinear evolution equations and painlevé test. World Scientific, Singapore, 1988
Tian, B., Gao, Y.T. Truncated painlevé expansion and a wide-ranging type of generalized variable-coefficient kadomtsev-petviashvili equations. Phys. Lett. A., 209(5):297–304 (1995)
Ŭgurlu, S. Y., Kart, C. The painlev é property and bäcklund transformation for fisher’s equation. Int. J. Comput. Numer. Anal. Appl., 3(3):297–303 (2003)
Weiss, J., Tabor, M., Carnevale, G. The painlevé property for partial differential equations. J. Math. Phys., 24(3):522–526 (1983)
Weiss, J.J. The painlevé property for partial differential equations. II. Math. Phys., Bäcklund Transformation, Lax Pairs, and the Schwarzian Derivative. 24(6):1405–1413 (1983)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Öğün, A., Kart, C. Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients. Acta Mathematicae Applicatae Sinica, English Series 23, 563–568 (2007). https://doi.org/10.1007/s10255-007-0395
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10255-007-0395
Keywords
- Nonlinear evolution equations
- fisher equation
- generalized fisher equation
- bäcklund transformation
- painlevé property