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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 220, Number 3, Pages 500–511
DOI: https://doi.org/10.4213/tmf10739 (Mi tmf10739) 		 
Gauge transformations between three-component KP and three-component mKP hierarchies

Lin Suna, Chuanzhong Lia, Ming Chena, Wei Liubc

a College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, China
b College of Mathematics and Information Science, Shandong Technology and Business University, Yantai, Shandong, China
c Yantai Key Laboratory of Big Data Modeling and Intelligent Computing, Yantai, Shandong, China
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DOI: https://doi.org/10.4213/tmf10739
Abstract: We examine the gauge transformations between the three-component Kadomtsev–Petviashvili (KP) hierarchy and the three-component modified Kadomtsev–Petviashvili (mKP) hierarchy. We introduce the auto-Bäcklund transformation of the three-component KP hierarchy and describe the Miura transformation of the three-component KP and mKP hierarchies, that is, $k=0\to k=1$. Additionally, the auto-Bäcklund transformation of the three-component mKP hierarchy is also given. This provides more powerful evidence that the gauge transformations generate Miura and auto-Bäcklund transformation on the eigenfunctions of the three-component KP and mKP hierarchies.
Keywords: gauge transformations, three-component KP hierarchy, three-component mKP hierarchy.
Funding agency Grant number
National Natural Science Foundation of China 12071237
Fundamental Research Projects of Science and Technology Innovation and Development Plan in Yantai City 2023YT06000660
This work is supported by the National Natural Science Foundation of China (grant No. 12071237) and Fundamental Research Projects of Science and Technology Innovation and Development Plan in Yantai City (grant No. 2023YT06000660).
Received: 08.04.2024
Revised: 26.04.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 220, Issue 3, Pages 1486–1495
DOI: https://doi.org/10.1134/S0040577924090058
Document Type: Article
MSC: 37K10, 37K05, 35Q53
Language: Russian
Citation: Lin Sun, Chuanzhong Li, Ming Chen, Wei Liu, “Gauge transformations between three-component KP and three-component mKP hierarchies”, TMF, 220:3 (2024), 500–511; Theoret. and Math. Phys., 220:3 (2024), 1486–1495
Citation in format AMSBIB
\Bibitem{SunLiChe24}
\by Lin~Sun, Chuanzhong~Li, Ming~Chen, Wei~Liu
\paper Gauge transformations between three-component KP and three-component mKP hierarchies
\jour TMF
\yr 2024
\vol 220
\issue 3
\pages 500--511
\mathnet{http://mi.mathnet.ru/tmf10739}
\crossref{https://doi.org/10.4213/tmf10739}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 220
\issue 3
\pages 1486--1495
\crossref{https://doi.org/10.1134/S0040577924090058}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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