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

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