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