  The interest in the Camassa-Holm equation inspired the search for various
generalizations of this equation with interesting properties and applications.
In this letter we deal with such a two-component integrable system of coupled
equations. First we derive the system in the context of shallow water theory.
Then we show that while small initial data develop into global solutions, for
some initial data wave breaking occurs. We also discuss the solitary wave
solutions. Finally, we present an explicit construction for the peakon
solutions in the short wave limit of system.
