An Integrable Matrix Camassa-Holm Equation

We present an integrable sl(2)-matrix Camassa-Holm (CH) equation. The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws. This equation includes two undetermined functions, which satisfy a system of constraint conditions and may be reduced to a lot of known multi-component peakon equations. We find a method to construct constraint condition and thus obtain many novel matrix CH equations. For the trivial reduction matrix CH equation we construct its N-peakon solutions. (paper)