Symmetries of the \(q\)-difference heat equation (Q1334978)

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.