Type-II hidden symmetries through weak symmetries for nonlinear partial differential equations
The type-II hidden symmetries are extra symmetries appearing when the number of variables in PDEq is reduced by a variable transformation found from a Lie symmetry of this PDE. The main of the goal of the article is to show that the provenance of the type II Lie point hidden symmetries found for differential equations can be explained by considering some weak symmetries or conditional symmetries of the original PDEq. The author focus his attention in weak symmetries of the PDEq with special differential constraint in order to determine the source of these type-II hidden symmetries. The main new result is that it can be identified the PDEq from which the type-II hidden symmetries are inherited by using as differential constraint the ''side condition'' from which the reduction has been derived. The author explain why some PDEq derived by \textit{B. Abraham-Shrauner} and \textit{K. S. Govinder} [J. Nonlinear Math. Phys. 13, No. 1--4, 612--622 (2006; Zbl 1110.35321)] by guessing do not gain the whole set of Lie symmetries.
scientific article; zbMATH DE number 5355972