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

Nianhua Li ; Q. P. Liu

Symmetry, integrability and geometry: methods and applications, Tome 18 (2022)

Résumé

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.

Détail

Mots-clés : soliton, Darboux transformation, Lax pair.

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