Near-monochromatic water waves on the sphere

We study analytically and numerically a class of traveling and standing wav es in a model of weakly non-linear gravity water waves on the sphere. These waves are 'near-monochromatic' in space, i.e. their amplitude consists of one spherical harmonic plus small corrections, and we see numerically that they retain this property for long time. A main feature of the model we con sider is that it possesses a Hamiltonian structure. This structure is prese rved by our numerical implementation, and we use formal and rigorous argume nts from classical perturbation theory to understand the numerical observat ions. (C)1999 Elsevier Science B.V. All rights reserved.