Traveling waves to a reaction-diffusion equation

Zhaosheng Feng

doi:10.3934/proc.2007.2007.382

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2007, Volume 2007: 382-390. Doi: 10.3934/proc.2007.2007.382 open access

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Traveling waves to a reaction-diffusion equation

Zhaosheng Feng^1,

1.
Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539

Received: September 2006

Revised: March 2007

Published: August 2007

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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.

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Mathematics Subject Classification: Primary: 34C05, 34C20; Secondary: 34C20.

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