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

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Journal Article
Journal of Differential Equations, 2017, 263 (11), pp. 7412 - 7447
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© 2017 Elsevier Inc. 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.
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