Lin Sun, Chuanzhong Li, Ming Chen, Wei Liu, “Gauge transformations between three-component KP and three-component mKP hierarchies”, TMF, 2024, Volume 220, Number 3,Pages <nobr>500

Gauge transformations between three-component KP and three-component mKP hierarchies

Lin Sun^a, Chuanzhong Li^a, Ming Chen^a, Wei Liu^bc

^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

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.

MSC: 37K10, 37K05, 35Q53

Received: 08.04.2024
Revised: 26.04.2024

DOI: 10.4213/tmf10739