### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 18 (2022), 066, 14 pages      arXiv:2202.03041      https://doi.org/10.3842/SIGMA.2022.066

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

Nianhua Li ab and Q.P. Liu c
a) School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P.R. China
b) Faculty of Mathematics, National Research University Higher School of Economics, 119048, Moscow, Russia
c) Department of Mathematics, China University of Mining and Technology, Beijing, 100083, P.R. China

Received February 08, 2022, in final form August 30, 2022; Published online September 04, 2022

Abstract
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.

Key words: soliton; Darboux transformation; Lax pair.

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