Conserved quantities and group classification of wave equation on hyperbolic space

This paper discusses the nonlinear wave equation on hyperbolic space. We extend some results reported in Nadjafikhah and Zaeim (2011) [17]. Partial Noether theorem is applied to the equation under consideration and partial Noether operators are computed for different cases of f ( u ) . Furthermore, these partial Noether operators are utilized to calculate corresponding conserved quantities. A complete group classification is discussed for the considered equation. Maximal solvable algebra of Lie point symmetries is used to reduce the class of considered equation. Then algebras of translational symmetries are associated with its infinite conservation laws.