Lie Group Symmetries as Integral Transforms of Fundamental Solutions

Mark Craddock and Kelly A Lennox
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Mark Craddock: Department of Mathematical Sciences, University of Technology Sydney

No 183, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We obtain fundamental solutions for PDEs of the form ut = x uxx +f(x)ux ??xru by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform.

Keywords: lie symmetry groups; fundamental solutions; transition densities; short range models; zero coupon bond pricing (search for similar items in EconPapers)
Pages: 23 pages
Date: 2006-09-01
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Citations: View citations in EconPapers (3)

Published as: Craddock, M. and Lennox, K. A., 2007, "Lie Group Symmetries as Integral Transforms of Fundamental Solutions", Journal of Differential Equations, 232(2), 652-674.

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