  The conserved quantities, that are, gravitational energy-momentum and its
relevant quantities are investigated for cylindrical and spherical
gravitational waves in the framework of teleparallel equivalent of General
Relativity using the Hamiltonian approach. For both cylindrical and spherical
gravitational waves, we obtain definite energy and constant momentum. The
constant momentum shows consistency with the results available in General
Relativity and teleparallel gravity. The angular momentum for cylindrical and
spherical gravitational waves also turn out to be constant. Further, we
evaluate their gravitational energy-momentum fluxes and gravitational pressure.
