Local-in-space blow-up and symmetric waves for a generalized two-component Camassa–Holm system

Abstract

In this paper, we consider a generalized two-component Camassa–Holm system, which can be derived from the theory of shallow water waves moving over a linear shear flow. We establish the new local-in-space blow-up criteria simplifying and extending the earlier blow-up criteria for the system. In particular, we show that symmetric water waves for the system are traveling waves.