Wave-like solutions for a class of parabolic models

A reduction aproach is developed for determining exact solutions of a nonlinear second order parabolic PDE. The method in point makes a complementary use of the leading ideas of the theory of quasilinear hyperbolic systems of first order endowed by differential constraints and of the techniques providing multiple wave-like solutions of nonlinear PDEs. The searched solutions exhibit a inherent wave features and they are obtained by solving a consistent overdetermined system of PDEs. Remarkably, in the process it is possible to define nonlinear model equations which allow special classes of initial or boundary value problems to be solved in a closed form. Within the present reduction approach exact solutions and model material response functions are obtained for an equation of widespread application in many fields of interest.