Affine and Finite Lie Algebras and Integrable Toda Field Equations on Discrete Space-Time

Symmetry Integrability and Geometry-Methods and Applications

article

Rustem Garifullin¹  Ismagil Habibullin¹  Marina Yangubaeva² 

[1] Ufa Institute of Mathematics, Russian Academy of Science;Faculty of Physics and Mathematics

关键词: af fine Lie algebra;    dif ference-dif ference systems;    S-integrability;    Darboux integrability;    Toda field theory;    integral;    symmetry;    Lax pair;   

DOI  :  10.3842/SIGMA.2012.062

来源: National Academy of Science of Ukraine

【 摘 要 】

Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras $A_N$, $B_N$, $C_N$, $G_2$, $D_3$, $A_1^{(1)}$, $A_2^{(2)}$, $D^{(2)}_N$ these systems are proved to be integrable. For the systems corresponding to the algebras $A_2$, $A_1^{(1)}$, $A_2^{(2)}$ generalized symmetries are found. For the systems $A_2$, $B_2$, $C_2$, $G_2$, $D_3$ complete sets of independent integrals are found. The Lax representation for the difference-difference systems corresponding to $A_N$, $B_N$, $C_N$, $A^{(1)}_1$, $D^{(2)}_N$ are presented.

【 授权许可】

Unknown