Cylindrical and spherical quantum ion acoustic waves
Abstract
Cylindrical and spherical deformed Kortewegde 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 onedimensional 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, Coochbehar736135 (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; KORTEWEGDE 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, Kolkata700108. 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, Kolkata700108. 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, Kolkata700108. 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, Kolkata700108},
abstractNote = {Cylindrical and spherical deformed Kortewegde 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 onedimensional 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}
}

Cylindrical and spherical amplitude modulation of quantum ionacoustic (QIA) envelope solitary waves in a dense quantum plasma comprised of electrons and ions is investigated. For this purpose, a onedimensional quantum hydrodynamic model and the Poisson equation are considered. By using the standard reductive perturbation technique, a modified nonlinear Schroedinger equation with the geometrical and the quantum effects is derived. The effect of quantum corrections and the effect due to the cylindrical and spherical geometries on the propagation of the QIA envelope solitary waves are examined. It is shown that there exists a modulation instability period depending on the quantum parameter,more »

Cylindrical and spherical ion acoustic waves in a plasma with nonthermal electrons and warm ions
Using the reductive perturbation technique, nonlinear cylindrical and spherical Kortewegde Vries (KdV) and modified KdV equations are derived for ion acoustic waves in an unmagnetized plasma consisting of warm adiabatic ions and nonthermal electrons. The effects of nonthermally distributed electrons on cylindrical and spherical ion acoustic waves are investigated. It is found that the nonthermality has a very significant effect on the nature of ion acoustic waves. 
Comment on 'Exact solutions of cylindrical and spherical dust ion acoustic waves' [Phys. Plasmas 10, 4162 (2003)]
Dusty plasmas have been found almost everywhere in the Universe. Sahu and Roychoudhury [Phys. Plasmas 10, 4162 (2003)] have done their interesting analytic work on the cylindrical dust ionacoustic waves, without enough guidance to the readers on other existing analytic results. Such lack of guidance turns out to be critical. We hereby try to make the story more complete in the sense that the model does have plenty of exact analytic solutions published already, and to present a brief review on some of them. For the dustionacoustic and dustacoustic modes supported by the space/laboratory dusty plasmas, we hereby picture outmore » 
Response to 'Comment on 'Exact solutions of cylindrical and spherical dust ion acoustic waves'' [Phys. Plasmas 12, 054701 (2005)]
It is shown that the similarity solution of cylindrical Kortewegde Vries equation given by Tian and Gao in their Comment on our paper can be obtained by the group analysis method using the same generators given in the paper by Sahu and Roychoudhury.