Wave breaking in a class of nonlocal dispersive wave equations.

Hailiang Liu, Iowa State University

The Korteweg de Vries (KdV) equation is well known as an approximation model for small amplitude and long waves in different physical contexts, but wave breaking phenomena related to short wavelengths are not captured in. We introduce a class of nonlocal dispersive wave equations which incorporate physics of short wavelength scales. The model is identified by the renormalization of an infinite dispersive differential operator and the number of associated conservation laws. Several well-known models are thus rediscovered. Wave breaking criteria are obtained for several typical models including the Burgers-Poisson system, the Camassa-Holm type equation.