论文标题
无单肌无线性方程和多体系统
Monodromy free linear equations and many-body systems
论文作者
论文摘要
我们进一步开发了多体系统的方法，基于发现某些线性部分差分和差异方程的存在条件，这些方程是非线性集成方程的辅助线性问题，例如KP，BKP，CKP和TODA晶格的不同版本。这些条件暗示着对非线性方程的奇异溶液的时间演变的方程，这是Calogero-Moser和Ruijsenaars-Schneider类型的可集成多体系统的运动方程。引入了一种新的多体系统，该系统控制着B型Toda晶格的椭圆溶液的动力学。
We further develop the approach to many-body systems based on finding conditions of existence of meromorphic solutions to certain linear partial differential and difference equations which serve as auxiliary linear problems for nonlinear integrable equations such as KP, BKP, CKP and different versions of the Toda lattice. These conditions imply equations of the time evolution for poles of singular solutions to the nonlinear equations which are equations of motion for integrable many-body systems of Calogero-Moser and Ruijsenaars-Schneider type. A new many-body system is introduced, which governs dynamics of poles of elliptic solutions to the Toda lattice of type B.
