Wave breaking for a periodic shallow water equation

The focus of this paper is on the blow-up of a recently derived one-dimensional shallow water equation which is formally integrable and can be obtained by approximating directly the Hamiltonian for Euler’s equations in the shallow water regime. Some new criteria guaranteeing the development of singularities in finite time for strong solutions with regular initial data are obtained for the periodic case.  2003 Elsevier Inc. All rights reserved.