Noether symmetries of vacuum classes of pp-waves and the wave equation (Q2830967)

In this paper the Noether symmetry properties and conservation laws of the wave equation on some vacuum classes of pp-waves are investigated. The authors determine the Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays. Applying the classification of different metric functions and adopting Noether's theorem, the authors determine generators for the wave equation and derive conserved forms. For the possible cases considered, there exist symmetry groups with dimension two, three, five, six and eight. It is shown that each of these symmetry groups are related to the isometries or conformal algebra of the respective metrics, and the symmetry groups contain the conformal symmetries of the space-time.