Breaking Waves and Solitary Waves for a Two‐Component Novikov System

ABSTRACT In this paper, we are concerned with two types of solutions of a two‐component Novikov system, which is a coupled Camassa‐Holm type system with cubic nonlinearity. The first type of solutions exhibits finite time singularity in the sense of wave breaking. We perform a refined analysis based on the local structure of the dynamics to provide a sufficient condition on the initial data to guarantee wave breaking. The other type of solutions which we investigate is solitary waves, we present the conditions for the existence of solitary waves.