Symmetries of theq-difference heat equation
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The symmetry operators of aq-difference analog of the heat equation in one space dimension are determined. They are seen to generate aq-deformation of the semidirect product of sl(2, ℝ) with the three-dimensional Weyl algebra. It is shown that this algebraic structure is preserved if differentq-analogs of the heat equation are considered. The separation of variables associated to the dilatation symmetry is performed and solutions involving discreteq-Hermite polynomials are obtained.
Mathematics Subject Classifications (1991)39-XX 81-XX
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- 1.Gasper, G. and Rahman, M.,Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.Google Scholar
- 2.Floreanini, R. and Vinet, L., Quantum algebras andq-special functions,Ann. Phys. 221 (1993), 53–79.Google Scholar
- 3.Miller, W.,Symmetry and Separation of Variables, Addison-Wesley, Reading, Mass, 1977.Google Scholar
- 4.Blumen, G. and Cole, J., The general similarity solution of the heat equation,J. Math. Mech. 18, 1025–1042 (1969); Kalnins, E. and Miller, W., Lie theory and separation of variables, 5: The equationsiU t +U xx = 0 andiU t +U xx −c/x 2 U = 0,J. Math. Phys. 15, 1728–1737 (1974).Google Scholar
- 5.Al-Salam, W. A. and Carlitz, L., Some orthogonalq-polynomials,Math. Nachr. 30, 47–61 (1965).Google Scholar
- 6.Floreanini, R. and Vinet, L., Quantum symmetries ofq-difference equations, CRM-preprint, 1994.Google Scholar