# Cylindrical and spherical quantum ion acoustic waves

## Abstract

Cylindrical and spherical deformed Korteweg-de Vries (dKdV) equations are derived for quantum ion acoustic waves in an unmagnetized two species quantum plasma system, comprised of electrons and ions, by the reductive perturbation technique in the weakly nonlinear limit. The properties of quantum ion acoustic solitary waves are studied taking into account the quantum mechanical effects in a nonplanar cylindrical or spherical geometry, which differs from one-dimensional planar geometry. Both analytical and numerical solutions of the dKdV equations are discussed in some detail. There exists a critical value of quantum parameters beyond which the quantum ion acoustic soliton collapses. It is also found that for the critical values of H, viz., H=2, some nontrivial analytical solution exists for both cylindrical and spherical dKdV equations.

- Authors:

- Department of Mathematics, Dinhata College, Coochbehar-736135 (India)
- (India)

- Publication Date:

- OSTI Identifier:
- 20960092

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2409527; (c) 2007 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; ANALYTICAL SOLUTION; CYLINDRICAL CONFIGURATION; ELECTRONS; GEOMETRY; ION ACOUSTIC WAVES; IONS; KORTEWEG-DE VRIES EQUATION; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; NUMERICAL SOLUTION; PERTURBATION THEORY; QUANTUM MECHANICS; QUANTUM PLASMA; SOLITONS

### Citation Formats

```
Sahu, Biswajit, Roychoudhury, Rajkumar, and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108.
```*Cylindrical and spherical quantum ion acoustic waves*. United States: N. p., 2007.
Web. doi:10.1063/1.2409527.

```
Sahu, Biswajit, Roychoudhury, Rajkumar, & Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108.
```*Cylindrical and spherical quantum ion acoustic waves*. United States. doi:10.1063/1.2409527.

```
Sahu, Biswajit, Roychoudhury, Rajkumar, and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108. Mon .
"Cylindrical and spherical quantum ion acoustic waves". United States.
doi:10.1063/1.2409527.
```

```
@article{osti_20960092,
```

title = {Cylindrical and spherical quantum ion acoustic waves},

author = {Sahu, Biswajit and Roychoudhury, Rajkumar and Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata-700108},

abstractNote = {Cylindrical and spherical deformed Korteweg-de Vries (dKdV) equations are derived for quantum ion acoustic waves in an unmagnetized two species quantum plasma system, comprised of electrons and ions, by the reductive perturbation technique in the weakly nonlinear limit. The properties of quantum ion acoustic solitary waves are studied taking into account the quantum mechanical effects in a nonplanar cylindrical or spherical geometry, which differs from one-dimensional planar geometry. Both analytical and numerical solutions of the dKdV equations are discussed in some detail. There exists a critical value of quantum parameters beyond which the quantum ion acoustic soliton collapses. It is also found that for the critical values of H, viz., H=2, some nontrivial analytical solution exists for both cylindrical and spherical dKdV equations.},

doi = {10.1063/1.2409527},

journal = {Physics of Plasmas},

number = 1,

volume = 14,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}