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

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  • 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.
    Mathematics Subject Classification: Primary: 34A05; 34C25-28; 34M55; 35Q51; 35Q53; Secondary: 58F05; 58F14; 58F30; 74B20; 74J30.


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