On the Traveling Wave Solutions for a Nonlinear Diffusion-Convection Equation: Dynamical System Approach

The existence of uncountably infinite global monotonic wavefront solutions and semi-wavefront solutions with bounded support is proved for a general nonlinear diffusion-convection equation. 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.

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Stochastic & Multiscale Modeling and Computation