三角Gaudin模型的精确可积时间离散的贝克隆变换
Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
摘要：
我们构造了一个三角经典Gaudin磁体的双参数贝克隆变换族。该方法紧密遵循E.Sklyanin和V.Kuznetsov（1998，1999）在一些开创性论文中介绍的方法，并利用三角和有理情况之间的密切关系。正如A.Hone，V.Kuznetsov和作者之一（O.R.）（2001）的贝克隆变换提出了显式辛映射，从他们的Lax表示。建立了XXZ海森堡链的（预期）联系，并在适当的极限下恢复了理性情况。它展示了如何获得一个“物理”变换映射到真实的变量。导出了插值哈密顿流，并给出了相应的数值迭代方法。
英文摘要：
We construct a two-parameter family of Bäcklund transformations for the trigonometric classical Gaudin magnet. The approach follows closely the one introduced by E.Sklyanin and V.Kuznetsov (1998,1999) in a number of seminal papers, and takes advantage of the intimate relation between the trigonometric and the rational case. As in the paper by A.Hone, V.Kuznetsov and one of the authors (O.R.) (2001) the Bäcklund transformations are presented as explicit symplectic maps, starting from their Lax representation. The (expected) connection with the XXZ Heisenberg chain is established and the rational case is recovered in a suitable limit. It is shown how to obtain a "physical" transformation mapping real variables into real variables. The interpolating Hamiltonian flow is derived and some numerical iterations of the map are presented.
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