We study the head-on collision of two solitary waves in a precompressed granular chain using the discrete element method. Our study takes the Toda chain solution as the initial condition for the simulations. The simulation covers the dynamical evolution of the collision process from the start of the incident wave to the end of the collision. The interaction has a central collision region of about five-grain width in which two solitary waves merge completely and share only one peak. Four stages, i.e., the pre-in-phase traveling stage, lag-phase collision state, lead-phase collision state, and post-in-phase traveling stage, are identified to describe the complex collision processes. Our results may be helpful for explaining the existence of long-lived solitary waves seen in the simulations by Takato and Sen [ Europhys. Lett. 100 (2012) 24003].

中文翻译：

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颗粒链中Toda格子模型描述的孤立波的正面碰撞

我们使用离散元方法研究了预压缩颗粒链中两个孤立波的正面碰撞。我们的研究将Toda链解决方案作为模拟的初始条件。仿真涵盖了从入射波的开始到碰撞结束的碰撞过程的动态演变。相互作用的中心碰撞区域大约为五粒宽度，其中两个孤立波完全合并并且仅共享一个峰。确定了四个阶段，即同相前行进阶段，滞后相碰撞状态，超前相碰撞状态和同相后行进阶段，以描述复杂的碰撞过程。我们的结果可能有助于解释在Takato和Sen [Europhys.com的模拟中看到的长寿命孤立波的存在。来吧 100（2012）24003]。