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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 3, Pages 451–466
DOI: https://doi.org/10.4213/tmf9949 (Mi tmf9949) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Obtaining multisoliton solutions of the $(2+1)$-dimensional Camassa–Holm system using Darboux transformations

Hui Mao

School of Mathematics and Statistics, Nanning Normal University, Nanning, China
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DOI: https://doi.org/10.4213/tmf9949
Abstract: We construct and study Darboux transformations for the $(2+1)$-dimensional Camassa–Holm system. We apply a reciprocal transformation that relates the $(2+1)$-dimensional Camassa–Holm system and the linear system associated with the modified Kadomtsev–Petviashvili hierarchy. Using three Darboux transformation operators, we obtain three types of solutions for the $(2+1)$-dimensional Camassa–Holm system, of which one is a multisoliton solution. In addition, we briefly discuss rational solutions.
Keywords: $(2+1)$-dimensional Camassa–Holm system, Darboux transformation, reciprocal transformation, soliton solution.
Funding agency Grant number
National Natural Science Foundation of China 11905110
11871471
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 and 11871471), 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: 01.07.2020
Revised: 04.08.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 3, Pages 1638–1651
DOI: https://doi.org/10.1134/S0040577920120065
Bibliographic databases:
Document Type: Article
MSC: 35C08
Language: Russian
Citation: Hui Mao, “Obtaining multisoliton solutions of the $(2+1)$-dimensional Camassa–Holm system using Darboux transformations”, TMF, 205:3 (2020), 451–466; Theoret. and Math. Phys., 205:3 (2020), 1638–1651
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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