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October  2010, 14(3): 1119-1138. doi: 10.3934/dcdsb.2010.14.1119

On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach

Jibin Li 1, and  Yi Zhang 1,

1. 

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004

Received  November 2009 Revised  January 2010 Published  July 2010

For a general nonlinear diffusion-convection equation, the existence of uncountably infinite many global monotonic wavefront solutions and semi-wavefront solutions with bounded support is proved. By using the method of planar dynamical systems, the dynamical behavior of the corresponding traveling wave system is discussed. For some concrete nonlinear diffusion-convection equations, more than thirty exact explicit parametric representations of the wavefront solutions, semi-wavefront solutions and unbounded traveling wave solutions are given.
Keywords: Nonlinear diffusion-convection equation; wavefront solution; kink wave solution; exact explicit solution; planar integrable system..
Mathematics Subject Classification: Primary: 34A05; 34C25-28; 34M55; 35Q51; 35Q53; Secondary: 58F05; 58F14; 58F30; 74B20; 74J3.
Citation: Jibin Li, Yi Zhang. On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 1119-1138. doi: 10.3934/dcdsb.2010.14.1119
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