A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov
equations that describe breaking waves is introduced. A classification of low-order
conservation laws, peaked travelling wave solutions, and Lie symmetries is presented for
this family. These classifications pick out a 1-parameter equation that has several interesting
features: it reduces to the Camassa-Holm and Novikov equations when the polynomial has
degree two and three; it has a conserved H 1 norm and it possesses N-peakon solutions …