标题： Tzitzeica孤子与相对论Calogero-Moser三体簇 显示英文标题

标题： Tzitzeica solitons vs. relativistic Calogero-Moser 3-body clusters

摘要： 我们建立了一种双曲相对论Calogero-Moser系统与Tzitzeica方程（也称为Dodd-Bullough-Zhiber-Shabat-Mikhailov方程）的一类孤立子解之间的联系。 在具有2N个粒子和$N$反粒子的相对论系统的6N维相空间$\Omega$中，存在一个2N维的Poincaré不变子流形$\Omega_P$，对应于$N$个自由粒子和$N$个处于基态的束缚粒子-反粒子对。 所考虑的Tzitzeica$N$孤立子tau函数是实值的，并通过在$\Omega_P$点上计算的对偶Lax矩阵得到。 这种对应关系导致了孤立子作为两个粒子和一个反粒子在其最低内部能量状态下的聚集体的图像。 显示英文摘要

摘要： We establish a connection between the hyperbolic relativistic Calogero-Moser systems and a class of soliton solutions to the Tzitzeica equation (aka the Dodd-Bullough-Zhiber-Shabat-Mikhailov equation). In the 6N-dimensional phase space $\Omega$ of the relativistic systems with 2N particles and $N$ antiparticles, there exists a 2N-dimensional Poincar\'e-invariant submanifold $\Omega_P$ corresponding to $N$ free particles and $N$ bound particle-antiparticle pairs in their ground state. The Tzitzeica $N$-soliton tau-functions under consideration are real-valued, and obtained via the dual Lax matrix evaluated in points of $\Omega_P$. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state.