Geometric Methods for some Nonlinear Wave Equations
A number of results related to the geometric interpretation of some dispersive nonlinear wave equations are presented. It is first described how some well-known shallow water equations arise geometrically as Euler equations for the geodesic flow on the Virasoro group endowed with certain right-invariant metrics. For one of these equations?the Camassa-Holm equation?we demonstrate how geometric meth