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Teoreticheskaya i Matematicheskaya Fizika, 2025, Volume 222, Number 1, Pages 150–160
DOI: https://doi.org/10.4213/tmf10799 (Mi tmf10799) 		 
Gauge transformations between reduced $q$-KP and reduced $q$-mKP hierarchies

Shilong Huang, Chuanzhong Li

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, China
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DOI: https://doi.org/10.4213/tmf10799
Abstract: We reduce the $q$-KP hierarchy and the $q$-mKP hierarchy. By using the link between the $q$-KP hierarchy and the $q$-mKP hierarchy, we obtain a relation between the $q$-KdV and the $q$-mKdV hierarchies, as well as a relation between the $q$-Boussinesq and $q$-mBoussinesq equations. The connection between them can also be established by a gauge transformation. We verify that when in the limit $q\to 1$, these relations correspond to the results for classical systems.
Keywords: $q$-deformation, $q$-KP hierarchy, $q$-mKP hierarchy, gauge transformation.
Funding agency Grant number
National Natural Science Foundation of China 12071237
Chuanzhong Li was supported by the National Natural Science Foundation of China under grant No. 12071237.
Received: 30.07.2024
Revised: 30.08.2024
Published: 16.01.2025
English version:
Theoretical and Mathematical Physics, 2025, Volume 222, Issue 1, Pages 131–139
DOI: https://doi.org/10.1134/S0040577925010106
Bibliographic databases:
Document Type: Article
MSC: 35Q51; 35Q15; 37K10
Language: Russian
Citation: Shilong Huang, Chuanzhong Li, “Gauge transformations between reduced $q$-KP and reduced $q$-mKP hierarchies”, TMF, 222:1 (2025), 150–160; Theoret. and Math. Phys., 222:1 (2025), 131–139
Citation in format AMSBIB
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\paper Gauge transformations between reduced $q$-KP and reduced $q$-mKP hierarchies
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\pages 150--160
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\jour Theoret. and Math. Phys.
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\pages 131--139
\crossref{https://doi.org/10.1134/S0040577925010106}
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