GRAVITY-WAVES ON THE SURFACE OF THE SPHERE

We propose a Hamiltonian model for gravity waves on the surface of a f luid layer surrounding a gravitating sphere. The general equations of motion are nonlocal and can be used as a starting point for simpler mo dels, which can be derived systematically by expanding the Hamiltonian in dimensionless parameters. In this paper, we focus on the small wav e amplitude regime. The first-order nonlinear terms can be eliminated by a formal canonical transformation. Similarly, many of the second or der terms can be eliminated. The resulting model has the feature that it leaves invariant several finite-dimensional subspace on which the m otion is integrable.