R. de la Llave, P. Panayotaros
Gravity waves on the surface of the sphere
(76K, Plain TeX)
ABSTRACT. We propose a Hamiltonian model for
gravity waves on the surface of a fluid layer
surrounding a gravitating sphere. The general
equations of motion are non-local and can be used as a
starting point for simpler model equations,
which can be derived systematically by expanding the
Hamiltonian functional. In this paper,
we study in detail
the small wave amplitude regime.
The first order non-linear terms can be eliminated
by a formal canonical transformation. Similarly, many of the
second order terms can be eliminated. The resulting model
has the feature that it leaves invariant several finite dimensional
subspaces on which the motion is integrable.