What question did this study set out to answer?

To derive and analyze first‐order continuum models for nonlinear dynamics of granular crystal lattices.

March 14, 2026

First‐Order Continuum Models for Nonlinear Dispersive Waves in the Granular Crystal Lattice

Puntos clave

To derive and analyze first‐order continuum models for nonlinear dynamics of granular crystal lattices.
Develop theoretical and numerical models for nonlinear wave dynamics.
Focus on solitary, periodic, and dispersive shock waves.
Utilize modulation theory and fitting techniques for analysis.
Conduct direct numerical simulations to validate models.
Models effectively predict dispersive shock waves in granular crystal lattices.
Good agreement between PDE predictions and discrete model simulations.
Valid even without precompression, highlighting their accuracy.

Resumen

ABSTRACT We derive and analyze, theoretically 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.

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