TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DIFFUSION–CONVECTION–REACTION MODELS

For a class of nonlinear diffusion–convection–reaction equations, corresponding to two families of heteroclinic orbits connecting two nodes of the traveling wave system, the existence of uncountably infinite many global monotonic and nonmonotonic wavefront solutions is discussed. By using the method of planar dynamical systems, the dynamical behavior of the corresponding traveling wave system is studied. Under some parametric conditions, exact explicit parametric representations of the monotonic and nonmonotonic kink wave solutions are given.