Lie group symmetries as integral transforms of fundamental solutions

Academic Press Inc Elsevier Science
Publication Type:
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 u(t) = sigma x(gamma)u(xx) + f(x)u(x) - mu x(r)u 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 rtansform or some other classical transform.
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