the existence of gravitational waves remains unsolve pending a serendipitous discovery.
But, as for the descriptions of all waves (tidal waves, light waves, sound waves, seismic waves, etc), these can be accomplished by solving the partial differential wave equation. As for the gravitons, their descriptions can be done by the quantum field version of the classical wave equation of higher than 4 dimensions.
Great question myphysics! The possibility of gravity waves is truly exciting. For the latest research in Gravity Waves including background material and links, visit this Gravity Probe B website. It's been in orbit for 64 weeks now.