Lie group symmetries as integral transforms of fundamental solutions

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Journal Article
Journal of Differential Equations, 2007, 232 (2), pp. 652 - 674
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We obtain fundamental solutions for PDEs of the form ut= σ xγux x+ f (x) ux- μ 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. © 2006 Elsevier Inc. All rights reserved.
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