an:00644778
Zbl 0805.39008
Floreanini, Roberto; Vinet, Luc
Symmetries of the \(q\)-difference heat equation
EN
Lett. Math. Phys. 32, No. 1, 37-44 (1994).
00021940
1994
j
39A10 81R99 33D45 33D80
\(q\)-difference heat equation; \(q\)-Hermite polynomials; symmetry operators; symmetry algebra; dilatation symmetry
The authors consider three \(q\)-difference analogs of the heat equation in one space dimension. The symmetry operators of these \(q\)-difference equations as well as relations defining a symmetry algebra are determined. (Note that all considered \(q\)-deformations of the heat equation have the same symmetry algebra). For the \(q\)-difference heat equation, which has symmetry operators of the simplest form, an interesting representation of solutions involving \(q\)-Hermite polynomials are obtained. For this purpose the authors perform the separation of variables associated to the dilatation symmetry.
E.Trofimtchouk (Kiev)