Wave breaking phenomenon for the generalized FORQ equation

Abstract

In this paper, we consider the generalized Fokas–Olver–Rosenau–Qiao equation (also called the ab-family of equation). The local well-posedness and blow-up scenario are investigated. Sufficient conditions on the initial data to guarantee wave breaking are established for b = 2. For b = 2 and 1/6 < a ≤ 1/3, we also show that if the initial momentum density is positive in a compact support and the length of the support is small enough, then wave breaking occurs.