We present a study of the dynamics of a system of masses connected by springs and repelling by a $1∕r$ potential in 1D. The present study focuses on the dynamics in the regime where the repulsive force dominates the dynamics of the system. We conjecture that such a system may be approximately modeled by an alignment of repelling rigid bar magnets that are sufficiently far apart from each other. We show that except for cases where the repulsive potential is very weak, most of the energy due to a velocity perturbation at system initiation of magnitude $v_0\left(0\right)$ generates a propagating solitary wave in the system. Dynamical simulations show that this solitary wave shows no measurable tendency to thermalize over extended simulation time scales, thereby yielding an effectively non-ergodic system. Part of the energy generates low-amplitude persistent oscillations which do not show any measurable interaction with the solitary wave. We find that the solitary wave propagation speed $v_{SW}\propto v_0^2$ for various coupling strengths. We further demonstrate that owing to the repulsion between the adjacent particles, these solitary waves are mutually repulsive, i.e., they cannot cross each other and hence there is no phase change associated with their mutual interactions. We use the data driven Dynamic Mode Decomposition technique to develop a simple approximate way to represent the propagating solitary wave. Additionally, we compute fluctuations in the kinetic energy of the system at late times and show that the energy fluctuations increase drastically when the effects of $v_0$ and the coupling associated with the repulsive interactions become competitive.

我们提出了一个由弹簧连接的质量系统的动力学研究，并由一个弹簧排斥。 $\mathrm{1个}∕\mathrm{[R}$一维的潜力。本研究的重点是在排斥力主导系统动力学的状态下的动力学。我们推测这样的系统可以通过相互排斥足够远的刚性钢条磁体的对准来近似建模。我们表明，除了排斥势很弱的情况外，大部分能量是由系统初始强度引起的速度扰动引起的$v_0（0）$在系统中生成传播的孤立波。动力学仿真表明，在延长的仿真时间范围内，孤波没有可测的热化趋势，从而产生了有效的非遍历系统。一部分能量会产生低振幅的持续振荡，该振荡不会显示出与孤立波的任何可测量的相互作用。我们发现孤波传播速度$v_{\mathrm{小号}\mathrm{w\; ^}}\propto v_0^2$各种耦合强度。我们进一步证明，由于相邻粒子之间的排斥，这些孤立波是相互排斥的，即它们无法彼此交叉，因此没有相互影响的相变。我们使用数据驱动的动态模式分解技术来开发一种简单的近似方法来表示传播的孤立波。此外，我们计算了系统晚些时候动能的波动，并表明当以下因素影响时，能量波动急剧增加$v_0$ 与排斥相互作用相关的耦合变得竞争。