TY - JOUR
AU - Zhang, Yufeng
AU - Yang, Xiao-Jun
PY - 2016
TI - Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations
JO - Journal of Nonlinear Sciences and Applications
SP - 6126--6141
VL - 9
IS - 12
AB - 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.
SN - ISSN 2008-1901
UR - http://dx.doi.org/10.22436/jnsa.009.12.18
DO - 10.22436/jnsa.009.12.18
ID - Zhang2016
ER -