  We present a reciprocal transformation which links the Geng-Xue equation to a
particular reduction of the first negative flow of the Boussinesq hierarchy. We
discuss two reductions of the reciprocal transformation for the
Degasperis-Procesi and Novikov equations, respectively. With the aid of the
Darboux transformation and the reciprocal transformation, we obtain a compact
parametric representation for the smooth soliton solutions such as multi-kink
solutions of the Geng-Xue equation.
