Wave propagation with longitudinal dust grain oscillations in dusty plasma crystals

Abstract

Traveling waves are studied with a longitudinal dust grain oscillation in dusty plasma crystals modeled by [Formula: see text]-Fermi Pasta Ulam Tsingou equation. Within the phonon band of the dispersion relation, the quasidiscrete approximation is applied to the relative displacement of the model to derive the nonlinear Schrödinger equation. The bright soliton solution is used as an initial condition for the full integration. The propagation of the robust bright wave is observed for the frequency far from the cutoff frequency while the localize wave is obtained at the cutoff frequency. In the forbidden bandgap, an analytical amplitude threshold of the nonlinear supratransmission phenomenon is derived. The numerical simulation confirms the validity of the analytical threshold, and the train of bright soliton is generated. Finally, by harmonically driving the equation of the longitudinal dusty plasma crystal, the traveling asymmetric bright soliton is generated for the first time from the plane wave.