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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 210, Number 2, Pages 199–212
DOI: https://doi.org/10.4213/tmf10182 (Mi tmf10182) 		 
Bäcklund transformation and applications for the Vakhnenko equation

Min  Xuea, Hui Maob

a Department of Mathematics, School of Science, China University of Mining and Technology, China
b School of Mathematics and Statistics, Nanning Normal University, Nanning, Guangxi, China
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DOI: https://doi.org/10.4213/tmf10182
Abstract: With the aid of the reciprocal transformation and the associated Vakhnenko equation, we construct and study a Bäcklund transformation (BT) involving both independent and dependent variables for the Vakhnenko equation. We derive the corresponding nonlinear superposition formula or $2$-BT and $3$-BT and rewrite them in terms of Pfaffians. We also discuss the representation for the general $N$-BT. As applications, some explicit solutions of the Vakhnenko equation are presented.
Keywords: Vakhnenko equation, Bäcklund transformation, nonlinear superposition formula, loop soliton solution.
Funding agency Grant number
National Natural Science Foundation of China 11871471
11931017
11905110
Natural Science Foundation of Guangxi Zhuang autonomous region 2018GXNSFBA050020
This work is supported by the National Natural Science Foundation of China (Grant Nos. 11871471, 11931017 and 11905110) and the Natural Science Foundation of Guangxi Zhuang autonomous region, China (Grant No. 2018GXNSFBA050020).
Received: 12.10.2021
Revised: 18.11.2021
English version:
Theoretical and Mathematical Physics, 2022, Volume 210, Issue 2, Pages 172–183
DOI: https://doi.org/10.1134/S0040577922020027
Bibliographic databases:
Document Type: Article
MSC: 35Q58, 37K10
Language: Russian
Citation: Min  Xue, Hui Mao, “Bäcklund transformation and applications for the Vakhnenko equation”, TMF, 210:2 (2022), 199–212; Theoret. and Math. Phys., 210:2 (2022), 172–183
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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