This article is cited in 4 papers

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

Nianhua Li^ab, Q. P. Liu<sup>c

a</sup> Faculty of Mathematics, National Research University Higher School of Economics, 119048, Moscow, Russia
^b School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P.R. China
^c Department of Mathematics, China University of Mining and Technology, Beijing, 100083, P.R. China

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.

Keywords: soliton, Darboux transformation, Lax pair.

MSC: 35Q51, 35C08, 37K10

Received: February 8, 2022; in final form August 30, 2022; Published online September 4, 2022

Language: English

DOI: 10.3842/SIGMA.2022.066

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ArXiv: 2202.03041