Abstract: A class of gravitational wave equation in the Vierbein representation of the local Lorentz group gravitational gauge theory are obtained. Finally,it is also proved that the equation contains the Bondi's plane wave equation and gravitational soliton equation, and the Bondi's plane wave (Sandwich waves)and gravitational soliton are some special solutions of the equation. Therefore, these solutions are in agreement with the quantum field theory.

Key words: Gravitational gauge theory, Diagonal metric, Gravitational wave equation, Bondi's plane waves, Gravitational soliton