Solitons and thermal fluctuations in strongly nonlinear solids

TL;DR

This paper investigates how solitary waves propagate in strongly nonlinear solids with thermal fluctuations, deriving analytical models and confirming them with numerical simulations, revealing new types of solitary waves.

Contribution

It introduces an effective Langevin equation for solitary waves in nonlinear chains and reports the discovery of expansion solitary waves in such systems.

Findings

Analytical damping rate and thermal diffusion for solitary waves.

Good agreement between analytical and numerical results.

Identification of expansion solitary waves (anti-solitons) in nonlinear chains.

Abstract

We study a chain of anharmonic springs with tunable power law interactions as a minimal model to explore the propagation of strongly non-linear solitary wave excitations in a background of thermal fluctuations. By treating the solitary waves as quasi-particles, we derive an effective Langevin equation and obtain their damping rate and thermal diffusion. These analytical findings compare favorably against numerical results from a Langevin dynamic simulation. In our chains composed of two sided non-linear springs, we report the existence of an expansion solitary wave (anti-soliton) in addition to the compressive solitary waves observed for non-cohesive macroscopic particles.