submitted on 2024-03-04, 05:09 and posted on 2024-03-04, 05:10authored byHassan Azad, Khaleel Anaya, Ahmad Al-Dweik, M. Mustafa
Algorithms to construct the optimal systems of dimension of at most three of Lie algebras are given. These algorithms are applied to determine the Lie algebra structure and optimal systems of the symmetries of the wave equation on static spherically symmetric spacetimes admitting G7 as an isometry algebra. Joint invariants and invariant solutions corresponding to three-dimensional optimal systems are also determined.