# Binary Bargmann symmetry constraint associated with $3\times 3$ discrete matrix spectral problem

Volume 8, Issue 5, pp 496--506
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### Authors

Xin-Yue Li - College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China. Qiu-Lan Zhao - College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China. Yu-Xia Li - Shandong Key Laboratory for Robot and Intelligent Technology, Qingdao 266590, P. R. China. Huan-He Dong - College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.

### Abstract

Based on the nonlinearization technique, a binary Bargmann symmetry constraint associated with a new discrete $3\times 3$ matrix eigenvalue problem, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals, is proposed. A new symplectic map of the Bargmann type is obtained through binary nonlinearization of the discrete eigenvalue problem and its adjoint one. The generating function of integrals of motion is obtained, by which the symplectic map is further proved to be completely integrable in the Liouville sense.

### Share and Cite

##### ISRP Style

Xin-Yue Li, Qiu-Lan Zhao, Yu-Xia Li, Huan-He Dong, Binary Bargmann symmetry constraint associated with $3\times 3$ discrete matrix spectral problem, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 496--506

##### AMA Style

Li Xin-Yue, Zhao Qiu-Lan, Li Yu-Xia, Dong Huan-He, Binary Bargmann symmetry constraint associated with $3\times 3$ discrete matrix spectral problem. J. Nonlinear Sci. Appl. (2015); 8(5):496--506

##### Chicago/Turabian Style

Li, Xin-Yue, Zhao, Qiu-Lan, Li, Yu-Xia, Dong, Huan-He. "Binary Bargmann symmetry constraint associated with $3\times 3$ discrete matrix spectral problem." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 496--506

### Keywords

• Discrete Hamiltonian structure
• binary Bargmann symmetry constraint
• finite-dimensional integrable system .

•  35Q51
•  37J15

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