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 |
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| Date: | 2022 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| 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| _version_ | 1862617882729381888 |
|---|---|
| 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.
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| first_indexed | 2026-03-14T10:23:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211722 |
| 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Smooth Multisoliton Solutions of a 2-Component Peakon System with Cubic Nonlinearity Article published earlier |
| 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 |