Traveling waves to a reaction-diffusion equation

Pages: 382 - 390, Issue Special, September 2007

 Abstract        Full Text (187.8K)              

Zhaosheng Feng - Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, United States (email)

Abstract: In this paper, we study a nonlinear reaction–diffusion equation for its traveling waves. This equation can be regarded as a generalization of the Fisher equation and is used as a nonlinear model, in the one-dimensional situation, for studying insect and animal dispersal with growth dynamics. Applying the Lie symmetry method, we obtain two traveling wave solutions under certain parametric conditions and express them in terms of elliptic functions.

Keywords:  Traveling wave, differential operator, Fisher equation, approximate solution, equilibrium point, decomposition method.
Mathematics Subject Classification:  Primary: 34C05, 34C20; Secondary: 34C20.

Received: September 2006;      Revised: March 2007;      Published: September 2007.