Work

A regularized continuum model for travelling waves and dispersive shocks of the granular chain

Year: 2025

Type: article

Abstract: In this paper, we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations. After revisiting earlier continuum approximations, we propose a regularized continuum model variant to approximate the discrete granular crystal model through a suitable partial differential equation. We then compute, both analytically and numerically, its travelling wave and periodic travelling wave solutions, in addition to its conservation laws. Next, using the periodic solutions, we describe quantitatively various features of the dispersive shock wave (DSW) by applying Whitham modulation theory and the DSW fitting method. Finally, we perform several sets of systematic numerical simulations to compare the corresponding DSW results with the theoretical predictions and illustrate that the continuum model provides a good approximation of the underlying discrete one.

Source: Journal of Nonlinear Waves

DOI: 10.1017/s3033426825000038

Authors: Su Yang, Gino Biondini, Christopher Chong, Panayotis G. Kevrekidis

Institutions: University of Massachusetts Amherst, University at Buffalo, State University of New York, Bowdoin College

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: National Science Foundation