# American Institute of Mathematical Sciences

August  2009, 24(3): 763-780. doi: 10.3934/dcds.2009.24.763

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

 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  April 2009

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.
Citation: Zhaosheng Feng, Goong Chen. Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 763-780. doi: 10.3934/dcds.2009.24.763
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