Type-II hidden symmetries of the linear 2D and 3D wave equations

Abstract

Type-II hidden symmetries of the linear, two-dimensional and three-dimensional wave equations are analysed. These hidden symmetries are Lie point symmetries that appear in addition to the inherited point symmetries when the number of independent and dependent variables of a partial differential equation is reduced by a Lie point symmetry. The provenance of these hidden symmetries of partial differential equations is identified to be the same as found recently for some nonlinear partial differential equations. The appearance of Type-II hidden symmetries depends not only on the Lie symmetries used but on the order in which the symmetries are applied. The presence of Type-II hidden symmetries of partial differential equations complicates the prediction of symmetry reductions based on the Lie algebra associated with the original Lie point symmetries.