Approximate Mei symmetries of pp-wave spacetimes

Abstract

In this paper, rst order approximate Mei symmetries of the geodetic
Lagrangian for some classes of the pp-wave spacetimes are obtained. These classes
of pp-wave spacetimes include plane wave spacetimes in which (i). H = 2x2(ii).
H = x2u2 (iii). H = 2x2u4 and for pp-wave spacetimes (iv). H = xn (where
H is called scale factor and is a constant). After that, approximate Mei invariants
are calculated corresponding to each case.

Classification of Painlevé type equations by the Mei symmetries and their exact solutions

“…The practical relevance of our study extends to various physical systems, including but not limited to general relativity [36,37], fluid dynamics, heat transfer, and wave propagation. For example, in fluid dynamics, the identification of invariants can aid in understanding and predicting flow patterns, temperature distributions, and energy transport, whereas in heat transfer, they provide insights into the behavior of temperature fields in complex materials.…”