Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

TL;DR

This paper revisits the nonlinear dynamics of longitudinal particle motion in lattices, specifically in dusty plasma crystals, predicting various localized excitations like kinks, breathers, and shocks, supported by a general theoretical framework.

Contribution

It introduces a general nonlinear wave theory for dust crystal lattices with arbitrary potentials and interaction ranges, predicting new localized excitations and connecting to experimental observations.

Findings

Dust crystals support nonlinear kink-shaped excitations propagating above sound speed.

Both compressive and rarefactive kink excitations are predicted.

Existence of breathers, wavepackets, and shocks in dust crystals is established.

Abstract

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form $\phi(r)$ and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed $v_0$. Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.