# Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

## Abstract

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KP and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.

- Authors:

- Department of Mathematics, Jadavpur University, Kolkata 700032 (India)
- Department of Applied Mathematics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009 (India)

- Publication Date:

- OSTI Identifier:
- 22600065

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 7; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COLLISIONLESS PLASMA; DISTURBANCES; DUSTS; ELECTRONS; EQUATIONS; ION ACOUSTIC WAVES; IONS; NONLINEAR PROBLEMS; PERTURBATION THEORY; POSITRONS; SOLUTIONS; STABILITY; THREE-DIMENSIONAL CALCULATIONS; WAVE PROPAGATION; WAVELENGTHS

### Citation Formats

```
Sardar, Sankirtan, Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com, and Das, K. P.
```*Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons*. United States: N. p., 2016.
Web. doi:10.1063/1.4956462.

```
Sardar, Sankirtan, Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com, & Das, K. P.
```*Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons*. United States. doi:10.1063/1.4956462.

```
Sardar, Sankirtan, Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com, and Das, K. P. Fri .
"Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons". United States.
doi:10.1063/1.4956462.
```

```
@article{osti_22600065,
```

title = {Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons},

author = {Sardar, Sankirtan and Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com and Das, K. P.},

abstractNote = {A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KP and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.},

doi = {10.1063/1.4956462},

journal = {Physics of Plasmas},

number = 7,

volume = 23,

place = {United States},

year = {Fri Jul 15 00:00:00 EDT 2016},

month = {Fri Jul 15 00:00:00 EDT 2016}

}