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Title: Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions

Abstract

The purpose of this paper is to present the recent work of Das et al. [J. Plasma Phys. 72, 587 (2006)] on the existence and stability of the alternative solitary wave solution of fixed width of the combined MKdV-KdV-ZK (Modified Korteweg-de Vries-Korteweg-de Vries-Zakharov-Kuznetsov) equation for the ion-acoustic wave in a magnetized nonthermal plasma consisting of warm adiabatic ions in a more generalized form. Here we derive the alternative solitary wave solution of variable width instead of fixed width of the combined MKdV-KdV-ZK equation along with the condition for its existence and find that this solution assumes the sech profile of the MKdV-ZK (Modified Korteweg-de Vries-Zakharov-Kuznetsov) equation, when the coefficient of the nonlinear term of the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation tends to zero. The three-dimensional stability analysis of the alternative solitary wave solution of variable width of the combined MKdV-KdV-ZK equation shows that the instability condition and the first order growth rate of instability are exactly the same as those of the solitary wave solution (the sech profile) of the MKdV-ZK equation, when the coefficient of the nonlinear term of the KdV-ZK equation tends to zero.

Authors:
; ;  [1]
  1. Department of Mathematics, Chittaranjan College, 8A Beniatola Lane, Kolkata-700 009 (India)
Publication Date:
OSTI Identifier:
21069827
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 14; Journal Issue: 9; Other Information: DOI: 10.1063/1.2772615; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ION ACOUSTIC WAVES; IONS; KORTEWEG-DE VRIES EQUATION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PLASMA; PLASMA INSTABILITY; SOLITONS; STABILITY; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Das, Jayasree, Bandyopadhyay, Anup, Das, K P, Department of Mathematics, Jadavpur University, Kolkata-700 032, and Department of Applied Mathematics, University of Calcutta, 92-Acharya Prfulla Chandra Road, Kolkata-700 009. Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions. United States: N. p., 2007. Web. doi:10.1063/1.2772615.
Das, Jayasree, Bandyopadhyay, Anup, Das, K P, Department of Mathematics, Jadavpur University, Kolkata-700 032, & Department of Applied Mathematics, University of Calcutta, 92-Acharya Prfulla Chandra Road, Kolkata-700 009. Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions. United States. https://doi.org/10.1063/1.2772615
Das, Jayasree, Bandyopadhyay, Anup, Das, K P, Department of Mathematics, Jadavpur University, Kolkata-700 032, and Department of Applied Mathematics, University of Calcutta, 92-Acharya Prfulla Chandra Road, Kolkata-700 009. 2007. "Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions". United States. https://doi.org/10.1063/1.2772615.
@article{osti_21069827,
title = {Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions},
author = {Das, Jayasree and Bandyopadhyay, Anup and Das, K P and Department of Mathematics, Jadavpur University, Kolkata-700 032 and Department of Applied Mathematics, University of Calcutta, 92-Acharya Prfulla Chandra Road, Kolkata-700 009},
abstractNote = {The purpose of this paper is to present the recent work of Das et al. [J. Plasma Phys. 72, 587 (2006)] on the existence and stability of the alternative solitary wave solution of fixed width of the combined MKdV-KdV-ZK (Modified Korteweg-de Vries-Korteweg-de Vries-Zakharov-Kuznetsov) equation for the ion-acoustic wave in a magnetized nonthermal plasma consisting of warm adiabatic ions in a more generalized form. Here we derive the alternative solitary wave solution of variable width instead of fixed width of the combined MKdV-KdV-ZK equation along with the condition for its existence and find that this solution assumes the sech profile of the MKdV-ZK (Modified Korteweg-de Vries-Zakharov-Kuznetsov) equation, when the coefficient of the nonlinear term of the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation tends to zero. The three-dimensional stability analysis of the alternative solitary wave solution of variable width of the combined MKdV-KdV-ZK equation shows that the instability condition and the first order growth rate of instability are exactly the same as those of the solitary wave solution (the sech profile) of the MKdV-ZK equation, when the coefficient of the nonlinear term of the KdV-ZK equation tends to zero.},
doi = {10.1063/1.2772615},
url = {https://www.osti.gov/biblio/21069827}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 9,
volume = 14,
place = {United States},
year = {Sat Sep 15 00:00:00 EDT 2007},
month = {Sat Sep 15 00:00:00 EDT 2007}
}