Infinite propagation speed for a two component Camassa-Holm equation

This paper is concerned with the solutions of a two-component generalisation of the Camassa-Holm equation. We examine the propagation behaviour of compactly supported solutions, namely whether solutions which are initially compactly supported will retain this property throughout their time of evolution. In the negative case, where we show that solutions have an infinite speed of propagation, we present a description of how the solutions retain weaker properties throughout their existence time, namely they decay at an exponentially fast rate for the duration of their existence.