Traveling water waves on a sphere

We study numerically a model of weakly non-linear water waves on the surfac e of a layer surrounding a gravitating sphere. The equations of motion are non-local and Hamiltonian and our numerical implementation preserves these structures. We focus on a class of traveling and standing waves that are "n ear-monochromatic" in space, i.e. waves whose amplitude consists of one sph erical harmonic plus small corrections. We observe that such motions are st able for long time, and we use methods from Hamiltonian dynamical systems t o understand the numerical observations theoretically. (C) 1999 Elsevier Sc ience B.V. All rights reserved.