Modulated wavepackets associated with longitudinal dust grain oscillations in a dusty plasma crystal

TL;DR

This paper investigates the nonlinear modulation of dust lattice waves in a dusty plasma crystal, revealing stability conditions and predicting asymmetric localized envelope modes due to nonlinear interactions.

Contribution

It introduces a continuum model for longitudinal dust lattice waves, analyzing their stability and predicting asymmetric envelope localized modes in dusty plasma crystals.

Findings

Long wavelength LDLWs are stable against modulation.

Shorter wavelengths may become modulationally unstable.

Asymmetric envelope localized modes are predicted.

Abstract

The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while shorter wavelengths may be unstable. The possibility for the formation and propagation of different envelope localized excitations is discussed. It is shown that the total grain displacement bears a (weak) constant displacement (zeroth harmonic mode), due to the asymmetric form of the nonlinear interaction potential. The existence of asymmetric envelope localized modes is predicted. The types and characteristics of these coherent nonlinear structures are discussed.