# Compacton solutions and (non)integrability for nonlinear evolutionary PDEs associated with a chain of prestressed granules

## TL;DR

This paper studies a nonlinear PDE related to pre-stressed granular chains, exploring its solitary wave solutions, stability, and integrability, with numerical simulations comparing continuous and discrete models.

## Contribution

It introduces a family of PDEs supporting compacton solutions derived from granular chains and analyzes their stability, integrability, and numerical behavior.

## Key findings

- PDE supports bright and dark compactons.
- Numerical simulations show stable propagation and interactions.
- Comparison with discrete model confirms continuous approximation validity.

## Abstract

We present the results of study of a nonlinear evolutionary PDE (more precisely, a one-parameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in question supports solitary waves of compression and rarefaction (bright and dark compactons) and can be written in Hamiltonian form. We investigate {\em inter alia} integrability properties of this PDE and its generalized symmetries and conservation laws. For the compacton solutions we perform a stability test followed by the numerical study. In particular, we simulate the temporal evolution of a single compacton, and the interactions of compacton pairs. The results of numerical simulations performed for our model are compared with the numerical evolution of corresponding Cauchy data for the discrete model of chain of pre-stressed elastic granules.