Energy Content of Colliding Plane Waves Using Approximate Noether Symmetries

We study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use the approximate Lie symmetry method for Lagrangians for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. In both cases, we show that no nontrivial first-order approximate symmetry generator exists.