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

Li, Xin-Yue¹ ; Zhao, Qiu-Lan¹ ; Li, Yu-Xia² ; Dong, Huan-He¹

¹ College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China
² Shandong Key Laboratory for Robot and Intelligent Technology, Qingdao 266590, P. R. China

Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 5, p. 496-506.

Résumé

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.

Détail

DOI : 10.22436/jnsa.008.05.05

Classification : 35Q51, 37J15
Keywords: Discrete Hamiltonian structure, binary Bargmann symmetry constraint, finite-dimensional integrable system .

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