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

TL;DR

This paper introduces new classes of non-convolution integral equations derived from Lie symmetry analysis of hyperbolic PDEs, providing solutions that help solve associated Cauchy problems.

Contribution

It presents novel non-convolution integral equations from Lie symmetry analysis and offers classical solution methods for these equations.

Findings

Derived new integral equations from symmetry analysis

Provided explicit solutions for these integral equations

Applied solutions to solve Cauchy problems for hyperbolic PDEs

Abstract

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.