Exact traveling wave solutions of fast reaction–diffusion–convectionequations based on the Lambert function W

Abstract

A particular function defined in terms of the Lambert function W is shown to serve as the basis for exact traveling wave solutions to several reaction–diffusion–convection​ (RDC) equations involving rational, non-linear diffusion terms. These represent a generalization of some previously considered “fast” RDC equations. Here, some equations and their solutions involving constant, linear and power law convection terms are derived. The first order differential equation solved by this particular function is an Abel equation of the second kind with constant coefficients. • The Lambert W function permits solutions to several fast RDC equations. • A novel solution involving logarithmic diffusion is presented. • A solution related to a transformation of the heat equation is also given. • Solutions to several generalizations of the Burgers–Huxley equation are given.