Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6422050 | Applied Mathematics and Computation | 2011 | 12 Pages |
Abstract
This paper provides analytical solutions to the generalized Fisher equation with a class of time varying diffusion coefficients. To accomplish this we use the Painlevé property for partial differential equations as defined by Weiss in 1983 in “The Painlevé property for partial-differential equations”. This was first done for the variable coefficient Fisher's equation by ÃÄün and Kart in 2007; we build on this work, finding additional solutions with a weaker restriction on the trial solution. We also use the same technique to find solutions to Fisher's equation with time-dependent coefficients for both diffusion and nonlinear terms. Lastly we compute specific solutions to illustrate their behaviors.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Jason F. Hammond, David M. Bortz,