Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth

Zhaosheng Feng; Goong Chen

doi:10.3934/dcds.2009.24.763

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2009, Volume 24, Issue 3: 763-780. Doi: 10.3934/dcds.2009.24.763

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Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth

Zhaosheng Feng^1, and
Goong Chen^2,

1.
Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78541
2.
Department of Mathematics, Texas A&M University, College Station, TX 77843

Received: December 2007

Revised: June 2008

Published: September 2009

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Abstract

In this paper, we study a model of insect and animal dispersal where both density-dependent diffusion and nonlinear rate of growth are present. We analyze the existence of bounded traveling wave solution under certain parametric conditions by using the qualitative theory of dynamical systems. An explicit traveling wave solution is obtained by means of the first integral method. Traveling wave solutions in parametric forms for three particular cases are established by the Lie symmetry method.

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Mathematics Subject Classification: Primary: 34C14, 35B05; Secondary: 34C05.

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