# 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 Schroedinger 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.

- Authors:

- Department of Physics, Arak-University, Arak, 38156-879 (Iran, Islamic Republic of)
- (Belgium) and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 20860428

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 13; Journal Issue: 12; Other Information: DOI: 10.1063/1.2400594; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; APPROXIMATIONS; CRYSTALS; DISPERSION RELATIONS; DUSTS; MODULATION; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERTURBATION THEORY; PLASMA; PLASMA WAVES; POLARIZATION; POTENTIAL ENERGY; SCHROEDINGER EQUATION; TWO-DIMENSIONAL CALCULATIONS; WAVE PACKETS; WAVE PROPAGATION; YUKAWA POTENTIAL

### Citation Formats

```
Farokhi, B., Kourakis, I., Shukla, P. K., Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum.
```*Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals*. United States: N. p., 2006.
Web. doi:10.1063/1.2400594.

```
Farokhi, B., Kourakis, I., Shukla, P. K., Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, & Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum.
```*Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals*. United States. doi:10.1063/1.2400594.

```
Farokhi, B., Kourakis, I., Shukla, P. K., Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent, and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum. Fri .
"Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals". United States.
doi:10.1063/1.2400594.
```

```
@article{osti_20860428,
```

title = {Nonlinear modulated dust lattice wave packets in two-dimensional hexagonal dust crystals},

author = {Farokhi, B. and Kourakis, I. and Shukla, P. K. and Universiteit Gent, Sterrenkundig Observatorium, Krijgslaan 281, B-9000 Gent and Institut fuer Theoretische Physik IV, Fakultaet fur Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum},

abstractNote = {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 Schroedinger 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.},

doi = {10.1063/1.2400594},

journal = {Physics of Plasmas},

number = 12,

volume = 13,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2006},

month = {Fri Dec 15 00:00:00 EST 2006}

}