Hui Mao, Gaihua Wang, “Bäcklund transformations for the Degasperis–Procesi equation”, TMF, 203:3 (2020), 365–379; Theoret. and Math. Phys., 203:3 (2020), 747

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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 203, Number 3, Pages 365–379
DOI: https://doi.org/10.4213/tmf9838 (Mi tmf9838)

This article is cited in 15 scientific papers (total in 15 papers)

Bäcklund transformations for the Degasperis–Procesi equation

Hui Mao^a, Gaihua Wang^b

^a School of Mathematics and Statistics, Nanning Normal University, Nanning, China
^b Department of Mathematics, China University of Mining and Technology, Beijing, China

Full-text PDF (563 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf9838

Abstract: We consider the Bäcklund transformation for the Degasperis–Procesi (DP) equation. Using the reciprocal transformation and the associated DP equation, we construct the Bäcklund transformation for the DP equation involving both dependent and independent variables. We also obtain the corresponding nonlinear superposition, which we use together with the Bäcklund transformation to derive some soliton solutions of the DP equation.

Keywords: Degasperis–Procesi equation, Bäcklund transformation, nonlinear superposition formula, soliton.

Funding agency	Grant number
National Natural Science Foundation of China	11905110 11871471 11931017
Natural Science Foundation of Guangxi Zhuang autonomous region	2018GXNSFBA050020
Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Guangxi Zhuang autonomous region	2019KY0417
This research is supported by the National Natural Science Foundation of China (Grant Nos. 11905110, 11871471, and 11931017), the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2018GXNSFBA050020), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Guangxi Zhuang Autonomous Region, China (Grant No. 2019KY0417).

Received: 22.10.2019
Revised: 26.11.2019

English version:
Theoretical and Mathematical Physics, 2020, Volume 203, Issue 3, Pages 747–750
DOI: https://doi.org/10.1134/S0040577920060045

Bibliographic databases:

Document Type: Article

MSC: 35C08

Language: Russian

Citation: Hui Mao, Gaihua Wang, “Bäcklund transformations for the Degasperis–Procesi equation”, TMF, 203:3 (2020), 365–379; Theoret. and Math. Phys., 203:3 (2020), 747–750

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This publication is cited in the following 15 articles:

Xiaoyong Li, Changzheng Qu, “Nonlocal symmetries of the Degasperis–Procesi equation”, Theoret. and Math. Phys., 222:1 (2025), 106–118
Chenglu Zhu, Lihua Wu, “Bäcklund transformation and soliton solutions for a generalized Wadati-Konno-Ichikawa equation”, MATH, 10:4 (2025), 7828
Gaihua Wang, “Multisoliton solutions of the two-component Camassa–Holm equation and its reductions”, Theoret. and Math. Phys., 214:3 (2023), 308–333
N. Li, “A new 3-component Degasperis–Procesi hierarchy”, Physica D: Nonlinear Phenomena, 449 (2023), 133763
F. Tan, L. Wu, “On the Bäcklund transformation of a generalized Harry Dym type equation”, Wave Motion, 120 (2023), 103162
N. Aziz, K. Ali, A. R. Seadawy, A. Bashir, S. T. R. Rizvi, “Discussion on couple of nonlinear models for Lie symmetry analysis, self adjointees, conservation laws and soliton solutions”, Opt. Quant. Electron., 55:3 (2023), 201
H. Mao, “Multi-soliton solutions for the two-component modified short pulse equation and its nonlocal reductions via Bäcklund transformations”, Eur. Phys. J. Plus, 138:8 (2023), 769
J.-X. Niu, R. Guo, J.-W. Zhang, “Solutions on the periodic background and transition state mechanisms for the higher-order Chen–Lee–Liu equation”, Wave Motion, 123 (2023), 103233
Min Xue, Hui Mao, “Bäcklund transformation and applications for the Vakhnenko equation”, Theoret. and Math. Phys., 210:2 (2022), 172–183
H. Lundmark, J. Szmigielski, “A view of the peakon world through the lens of approximation theory”, Physica D: Nonlinear Phenomena, 440 (2022), 133446
H. Mao, Y. Miao, “Bäcklund transformation and nonlinear superposition formula for the two-component short pulse equation”, J. Phys. A: Math. Theor., 55:47 (2022), 475207
S. Huang, H. Li, “Darboux transformations of the Camassa-Holm type systems”, Chaos, Solitons & Fractals, 157 (2022), 111910
Hui Mao, “Novikov equation: Bäcklund transformation and applications”, Theoret. and Math. Phys., 206:2 (2021), 163–173
Shilong Huang, Hongmin Li, “Darboux Transformations of the Camassa-Holm Type Systems”, SSRN Journal, 2021
Mao H., Liu Q.P., “The Short Pulse Equation: Backlund Transformations and Applications”, Stud. Appl. Math., 145:4 (2020), 791–811

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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