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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 175, Number 2, Pages 178–192
DOI: https://doi.org/10.4213/tmf8374 (Mi tmf8374) 		 
The generalized Kupershmidt deformation for constructing new discrete integrable systems

Yehui Huanga, Runliang Linb, Yuqin Yaoc, Yunbo Zengb

a School of Mathematics and Physics, North China Electric Power University
b Department of Mathematical Sciences, Tsinghua University, Beijing, China
c Department of Applied Mathematics, China Agricultural University, Beijing, China
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DOI: https://doi.org/10.4213/tmf8374
Abstract: It is known that the KdV6 equation can be represented as the Kupershmidt deformation of the KdV equation. We propose a generalized Kupershmidt deformation for constructing new discrete integrable systems starting from the bi-Hamiltonian structure of a discrete integrable system. We consider the Toda, Kac–van Moerbeke, and Ablowitz–Ladik hierarchies and obtain Lax representations for these new deformed systems. The generalized Kupershmidt deformation provides a new way to construct discrete integrable systems.
Keywords: Kupershmidt deformation, bi-Hamiltonian system, discrete integrable system.
Received: 03.06.2012
Revised: 06.12.2012
English version:
Theoretical and Mathematical Physics, 2013, Volume 175, Issue 2, Pages 596–608
DOI: https://doi.org/10.1007/s11232-013-0049-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yehui Huang, Runliang Lin, Yuqin Yao, Yunbo Zeng, “The generalized Kupershmidt deformation for constructing new discrete integrable systems”, TMF, 175:2 (2013), 178–192; Theoret. and Math. Phys., 175:2 (2013), 596–608
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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