EXACT SOLUTIONS FOR NONLINEAR PDES VIA HERMITE POLYNOMIALS

In this note we construct exact solutions for nonlinear partial differential equations by means of Hermite polynomials. In particular, we consider generalized Burgers equations, that can be linearized by means of a Cole-Hopf-type transform. We show that it is possible to construct an interesting particular solution by using Hermite polynomials. We also consider a class of non-linear equations admitting isochronous solutions. The main aim is to show that Hermite polynomials can be used to construct exact solutions for a wide class of nonlinear integro-differential equations including nonlinear fractional equations.