A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations
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Authors
Huanhe Dong
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.
- Key Laboratory for Robot and Intelligent Technology of Shandong Province, Qingdao, 266510, P. R. China.
Tingting Chen
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.
Longfei Chen
- School of Economics, Shanghai University, Shanghai 200444, P. R. China.
Yong Zhang
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China.
Abstract
A discrete matrix spectral problem is proposed, the hierarchy of discrete integrable system is inferred,
which are Liouville integrable. And the Hamiltonian structures of the hierarchy are constructed. A family of
finite-dimensional completely integrable systems and a new integrable symplectic map are provided in terms
of the binary nonlinearity of spectral problem. In particular, two explicit formulations are acquired under
the condition of the bargmann constraints. After that, the symmetry of the discrete integrable systems is
given on the basis of the seed symmetry and its prolongation. Moreover, the solution of the discrete lattice
equation can be gained by the way of the infinitesimal generator.
Share and Cite
ISRP Style
Huanhe Dong, Tingting Chen, Longfei Chen, Yong Zhang, A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 7, 5107--5118
AMA Style
Dong Huanhe, Chen Tingting, Chen Longfei, Zhang Yong, A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations. J. Nonlinear Sci. Appl. (2016); 9(7):5107--5118
Chicago/Turabian Style
Dong, Huanhe, Chen, Tingting, Chen, Longfei, Zhang, Yong. "A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations." Journal of Nonlinear Sciences and Applications, 9, no. 7 (2016): 5107--5118
Keywords
- Symplectic map
- symmetry
- discrete integrable system
- liouville integrability
- nonlinearization.
MSC
- 35Q51
- 37K40
- 58J70
- 35A35
- 22E65
- 70H33
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