Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals

Abstract

The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schrödinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a “dressed” potential energy, taking into account interaction and geometric nonlinearities.

Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

“…Note that the friction term introduced on the left-hand-side of the equation of motion (11) and its continuum version (21), leads to the appearance of the damping rate ν (due to dustneutral collisions) in the dispersion relations (16)- (18). Dissipation in dusty plasma experiments is admittedly always present, yet may acquire very small values, depending on plasma density and pressure [Ref.…”

The particle-wake interactions in a hexagonal twodimensional dust lattice

“…Then we set the determinant of coefficients of Eqs. (17)(18)(19), it gives the dispersion relation as a third rank polynomial versus 2 ω . In limitation conditions when eliminating the wake ion effect, results of this paper converges to the results of, B. Farokhi et al [17] and S. V. Vladimirov et al [18].…”

“…In fundamental physics the most surprising discovery was the observation of crystal-like structures. Such plasma crystal structures can support longitudinal and transverse vibrational modes, which have been extensively studied in the last years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Dust lattice waves (DLW's) are produced by the oscillations of regularly spaced charged micrometer sized particles suspended in a plasma (plasma crystals), and there have been many publications on experimental and theoretical investigations of the DL modes in one-and twodimensional (1D and 2D) crystals [3][4][5][6][7][8][9][10][11][12][13].…”

Localized excitations in dusty plasma crystals: on the interface among plasma physics and nonlinear lattice theories

“…In 2D, hexagonal dust lattices sustain modulated envelope bell-shaped structures, which may be formed as a result of modulational instability of in-plane vibrations [18]. Discrete dust-lattice modes.…”