标题： 一阶连续介质模型用于颗粒晶体晶格中的非线性色散波 显示英文标题

标题： First-order continuum models for nonlinear dispersive waves in the granular crystal lattice

摘要： 我们通过分析和数值方法，推导并分析了两个一阶连续模型，以近似颗粒晶体晶格的非线性动力学，特别关注孤立波、周期波和色散冲击波。 由两个连续模型预测的色散冲击波通过调制理论、DSW拟合技术和直接数值模拟进行了研究。 基于偏微分方程的预测与颗粒晶格离散模型模拟生成的DSWs表现出良好的一致性，即使在没有预压缩的情况下，晶格仅具有非线性特性时也是如此。 这种有效的描述可能对未来更易于解析的原始晶格系统的近似方法有所帮助。 显示英文摘要

摘要： We derive and analyze, analytically and numerically, two first-order continuum models to approximate the nonlinear dynamics of granular crystal lattices, focusing specifically on solitary waves, periodic waves, and dispersive shock waves. The dispersive shock waves predicted by the two continuum models are studied using modulation theory, DSW fitting techniques, and direct numerical simulations. The PDE-based predictions show good agreement with the DSWs generated by the discrete model simulation of the granular lattice itself, even in cases where no precompression is present and the lattice is purely nonlinear. Such an effective description could prove useful for future, more analytically amenable approximations of the original lattice system.