New classes of non-convolution integral equations arising from Lie symmetry analysis of hyperbolic PDEs

Mark Craddock, Semyon Yakubovich

Published 2015-09-21Version 1

In this paper we consider some new classes of integral equations that arise from Lie symmetry analysis. Specifically, we consider the task of obtaining solutions of a Cauchy problem for some classes of second order hyperbolic partial differential equations. Our analysis leads to new integral equations of non-convolution type, which can be solved by classical methods. We derive solutions of these integral equations, which in turn lead to solutions of the associated Cauchy problems.