Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity

Abstract

We present a reciprocal transformation that 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.