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02/06/03 Colloquium
DR. TARAS LAKOBA
Department of Mathematics, University of Central Florida
Department of Mathematics, University of Central Florida
Perturbation Theory for the Benjamin-Ono Equation
Abstract: The Benjamin-Ono (BO) equation describes propagation of long waves at an interface between two layers of fluid of distinct densities. This equation in exactly integrable by the method of the Inverse Scattering Transform (IST); however, the IST for the BO has features not present in the corresponding techniques developed for other integrable evolution equations in one spatial dimension. In this talk, I will describe essential details of the IST and explain how this method can be used to develop a perturbation theory for an integrable equation. Then I will present highlights of the perturbation theory for the BO and emphasize its differences from perturbation theories for other integrable equations.