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

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 Dar...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2022
Main Authors: Li, Nianhua, Liu, Q.P.
Format: Article
Language:English
Published: Інститут математики НАН України 2022
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211722
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity. Nianhua Li and Q.P. Liu. SIGMA 18 (2022), 066, 14 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Li, Nianhua
Liu, Q.P.
author_facet Li, Nianhua
Liu, Q.P.
citation_txt Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity. Nianhua Li and Q.P. Liu. SIGMA 18 (2022), 066, 14 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
first_indexed 2026-03-14T10:23:49Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-14T10:23:49Z
publishDate 2022
publisher Інститут математики НАН України
record_format dspace
spelling Li, Nianhua
Liu, Q.P.
2026-01-09T12:46:03Z
2022
Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity. Nianhua Li and Q.P. Liu. SIGMA 18 (2022), 066, 14 pages
1815-0659
2020 Mathematics Subject Classification: 35Q51; 35C08; 37K10
arXiv:2202.03041
https://nasplib.isofts.kiev.ua/handle/123456789/211722
https://doi.org/10.3842/SIGMA.2022.066
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.
We are grateful to the anonymous referees for their suggestive comments. This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11805071, 11871471, and 11931107). N.L. is grateful to HSE for supporting his visit from August 2019 to September 2020, and especially would like to thank Ian Marshall and Maxim Pavlov for their hospitality.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
Article
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spellingShingle Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
Li, Nianhua
Liu, Q.P.
title Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
title_full Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
title_fullStr Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
title_full_unstemmed Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
title_short Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity
title_sort smooth multisoliton solutions of a 2-component peakon system with cubic nonlinearity
url https://nasplib.isofts.kiev.ua/handle/123456789/211722
work_keys_str_mv AT linianhua smoothmultisolitonsolutionsofa2componentpeakonsystemwithcubicnonlinearity
AT liuqp smoothmultisolitonsolutionsofa2componentpeakonsystemwithcubicnonlinearity