Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations
- College of Mathematics, China University of Mining and Technology, Xuzhou 221116, P. R. China.
- School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
- State Key Laboratory for Geo-Mechanics and Deep Underground Engineering, China University of Mining and Technology, 221116, P. R. China.
With the help of infinite-dimensional Lie algebras and the Tu scheme, we address a discrete integrable
hierarchy to reduce the generalized relativistic Toda lattice (GRTL) system containing the relativistic Toda
lattice equation and its generalized lattice equation. Meanwhile, the Riemann theta functions are utilized
to present its algebro-geometric solutions. Besides, a reduced spectral problem is given to find an integrable
discrete hierarchy obtained via R-matrix theory, which can be reduced to the Toda lattice equation and a
generalized Toda lattice (GTL) system. The Lax pair and the infinite conservation laws of the GTL system
are also derived. Finally, the Hamiltonian structure of the GTL system is generated by the Poisson tensor.
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Yufeng Zhang, Xiao-Jun Yang, Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6126--6141
Zhang Yufeng, Yang Xiao-Jun, Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations. J. Nonlinear Sci. Appl. (2016); 9(12):6126--6141
Zhang, Yufeng, Yang, Xiao-Jun. "Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6126--6141
- Spectral problem
- algebro-geometric solution
- Hamiltonian structure.
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