Abstract
In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations (PDEs) with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu’s method, in differential equations.
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(Communicated by Hong-qing ZHANG)
Project supported by the Ph. D. Programs Foundation of Ministry of Education of China (No. 20070128001), the Expenditure Budget program of Shanghai Municipal Education Commission (No. 2008069), the Innovation Program of Shanghai Municipal Education Commission (No. 09YZ239), and the Natural Science Foundation of Inner Mongolia (No. 200607010103)
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Temuer, C., Bai, Ys. Differential characteristic set algorithm for the complete symmetry classification of partial differential equations. Appl. Math. Mech.-Engl. Ed. 30, 595–606 (2009). https://doi.org/10.1007/s10483-009-0506-6
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DOI: https://doi.org/10.1007/s10483-009-0506-6