Lax representation and complete integrability for the periodic relativistic Toda lattice
Lax representation and complete integrability for the periodic relativistic Toda lattice
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DOI：
10.1016/0375-9601(89)90736-6
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发表时间：
1989-01
影响因子：
2.6
通讯作者：
M. Bruschi;O. Ragnisco
中科院分区：
文献类型：
--
作者：
M. Bruschi;O. Ragnisco
我们提出了周期相对论户田晶格的三种可能的Lax表示。第一个定理是有限非周期情形下定理的最自然推广[1，2]。第二种方法是最方便的方法，它不仅能推广无穷大情形，而且能推广无穷大情形的非交换和二维推广。第三种方法涉及自伴谱问题，可以看作是非相对论性户田格点的Flaschka表示的自然“相对论性”扩展，证明了系统的完全可积性.
We present three possible Lax representations for the periodic relativistic Toda lattice. The first one is the most natural extension ofthe one holding in the finite non-periodic case [1, 2]. The second one seemsthe most convenient to handlethe infinitecase, as well as its non-abelian and two-dimensional generalizations. The third one, which involves a self-adjoint spectral problem, and can be considered as the natural “relativistic” extension of the original Flaschka representation for the non-relativistic Toda lattice, turns out to be the proper one to prove the complete integrability of the system.