Abstract
We derive the Lie point symmetries of geodesic equations and and Noether gauge symmetries of the geodesic Lagrangian for some classes of pp-wave spacetimes. The considered classes of pp-wave spacetimes are the plane-wave spacetimes (i) , (ii) and (iii) , and a pp-wave spacetime (iv) , where H is the scale factor in pp-wave spacetime. We discuss the relations between the obtained Lie point and Noether gauge symmetry generators. We also calculate the first integrals in each of the cases, and give a solution of geodesic equations using those first integrals in case (i) as an example.
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