An algorithmic method for showing existence of nontrivial non-classical symmetries of partial differential equations without solving determining equations |
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Authors: | Temuer Chaolu G. Bluman |
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Affiliation: | 1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China;2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T1Z2, Canada |
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Abstract: | In this paper, based on differential characteristic set theory and the associated algorithm (also called Wu?s method), an algorithmic method is presented to decide on the existence of a nontrivial non-classical symmetry of a given partial differential equation without solving the corresponding nonlinear determining system. The theory and algorithm give a partial answer for the open problem posed by P.A. Clarkson and E.L. Mansfield in [21] on non-classical symmetries of partial differential equations. As applications of our algorithm, non-classical symmetries and corresponding invariant solutions are found for several evolution equations. |
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Keywords: | Non-classical symmetry Partial differential equations Differential characteristic set Existence Algorithm |
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