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A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy

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Abstract

By means of the nonlinearization technique, a Bargmann constraint associated with a new discrete \(4 \times 4\) matrix eigenvalue problem is proposed, and a new symplectic map of the Bargmann type is obtained through binary nonlinearization of the discrete eigenvalue problem and its adjoint one. Moreover, 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. Finally, the involutive representation of solutions are given.

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Acknowledgments

The first two authors are very grateful to prof. W. X. Ma for his enthusiastic guidance and discussion in the period of visiting University of south Florida. The work was supported by the Nature Science Foundation of China (Grant No. 61473177), the Nature Science Foundation of Shandong Province of China (Grant No. ZR2012AQ015) and the Science and Technology plan project of the Educational Department of Shandong Province of China (Grant No. J12LI03).

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Authors and Affiliations

  1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Qiu-lan Zhao & Xin-Yue Li

  2. Shandong Key Laboratory of Robotics and Intelligent Technology, Qingdao, 266590, People’s Republic of China

    Xin-Yue Li

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  1. Qiu-lan Zhao
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  2. Xin-Yue Li
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Correspondence to Xin-Yue Li.

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Zhao, Ql., Li, XY. A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy. Anal.Math.Phys. 6, 237–254 (2016). https://doi.org/10.1007/s13324-015-0116-2

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  • DOI: https://doi.org/10.1007/s13324-015-0116-2

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