# Nonlinear dispersive waves in repulsive lattices

## TL;DR

This paper investigates nonlinear wave propagation in a lattice of repelling particles through theoretical analysis and experiments, revealing mode conversion, dispersion effects, and acoustic dilatation, with implications for similar nonlinear systems.

## Contribution

It introduces an experimental setup with coupled magnetic dipoles and compares observed phenomena with $eta$-FPU theoretical predictions, highlighting new insights into nonlinear dispersive waves in repulsive lattices.

## Key findings

- Demonstrated mode conversion into higher harmonics influenced by dispersion.
- Predicted and discussed acoustic dilatation of the chain.
- Validated theoretical models with experimental results.

## Abstract

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting in an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of $\alpha$-FPU equation, describing a chain of masses connected by nonlinear quadratic springs. The results can be extrapolated to other systems described by this equation.