Backward-wave propagation with vertical dust grain oscillations in dusty plasma crystals

Abstract

We study the propagation of vertical dust grain oscillations in dusty plasma crystals. Applying the quasidiscrete approximation on the model of the dusty plasma crystal [see I. Kourakis and P. K. Shukla, Phys. Plasmas 12, 014502 (2005)], we derive a nonlinear Schrödinger equation and find that the system supports bright and dark soliton solutions. Also, it appears contrary to existing work that the lattice has a zero-dispersion frequency which induces the resonance of the nonlinear coefficient. The numerical integration of the equation of the model and the energy density confirm the backward-wave predicted by the dispersion relation and the fact that the phase and group velocities are antiparallel.