Type-II Hidden Symmetries for Some Nonlinear Partial Differential Equations

Abstract

The Type-II hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a Lie point symmetry. In this paper we analyze the connection between one of the methods analyzed in Abraham-Shrauner and Govinder (J. Nonlinear Math. Phys. 13:612, 2006) and the weak symmetries of the partial differential equation in order to determine the source of these hidden symmetries. We have considered some of the models presented in Abraham-Shrauner and Govinder (J. Nonlinear Math. Phys. 13:612, 2006), as well as a linear three-dimensional wave equation considered in Abraham-Shrauner et al. (J. Phys. A, Math. Theor., 39:5739, 2006).