Construction of new integrable systems and methods of their investigation is one of the main directions of development of the modern mathematical physics. Here we present an approach based on the study of behavior of roots of functions of canonical variables with respect to a parameter of simultaneous shift of space variables. Dynamics of singularities of the KdV and Sinh–Gordon equations, as well as rational cases of the Calogero–Moser and Ruijsenaars–Schneider models are shown to provide examples of such induced dynamics. Some other examples are given to demonstrates highly nontrivial collisions of particles and Liouville integrability of induced dynamical systems.

中文翻译：

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诱导动力学

构建新的可积系统及其研究方法是现代数学物理学发展的主要方向之一。在这里，我们提出了一种基于研究规范变量函数根相对于空间变量同时移动参数的行为的方法。显示了 KdV 和 Sinh-Gordon 方程的奇点动力学，以及 Calogero-Moser 和 Ruijsenaars-Schneider 模型的合理情况，以提供此类诱导动力学的示例。给出了一些其他例子来证明粒子的高度非平凡碰撞和诱导动力系统的刘维尔可积性。