Peakon and kink solutions for a system of 0-Holm-Staley equations

In this paper we consider a two-component system of the Holm-Staley equation with no stretching and a one-parameter nonlinearity in the convection term. Point symmetries are found, conditions for the existence of multipeakon and multikink solutions are determined. Solutions for the 1-peakon and 1-kink are explicitly obtained and they exhibit a behaviour quite different of their analogous in the scalar equation.