98-440 Panayotis Panayotaros

Near-monochromatic water waves on the sphere (77K, TeX) Jun 12, 98

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Abstract. We study analytically and numerically a class of traveling and standing waves 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 consider is that it possesses a Hamiltonian structure. This structure is preserved by our numerical implementation, and we use formal and rigorous arguments from classical perturbation theory to understand the numerical observations.

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