The stability of obliquely-propagating solitary-wave solutions to Zakharov-Kuznetsov-type equations

E.J. Parkes, S. Munro

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In certain circumstances, small amplitude, weakly nonlinear ion-acoustic waves in a magnetized plasma are governed by a Zakharov-Kuznetsov equation or by a reduced form of the equation. Both equations have a plane solitary travelling-wave solution that propagates at an angle αto the magnetic field. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the initial growth rate of a small, transverse, long-wavelength perturbation to these solitary-wave solutions. Previous results in the literature are corrected. A numerical determination of the growth rate is given. For k[mid R:] secα[mid R:][double less-than sign]1, where k is the wavenumber of the perturbation, there is excellent agreement between our analytical and numerical results.
LanguageEnglish
Pages695-708
Number of pages13
JournalJournal of Plasma Physics
Volume71
Issue number5
DOIs
Publication statusPublished - Oct 2005

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solitary waves
perturbation
ion acoustic waves
traveling waves
magnetic fields
wavelengths

Keywords

  • solitary-wave solutions
  • equations
  • plasma physics

Cite this

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abstract = "In certain circumstances, small amplitude, weakly nonlinear ion-acoustic waves in a magnetized plasma are governed by a Zakharov-Kuznetsov equation or by a reduced form of the equation. Both equations have a plane solitary travelling-wave solution that propagates at an angle αto the magnetic field. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the initial growth rate of a small, transverse, long-wavelength perturbation to these solitary-wave solutions. Previous results in the literature are corrected. A numerical determination of the growth rate is given. For k[mid R:] secα[mid R:][double less-than sign]1, where k is the wavenumber of the perturbation, there is excellent agreement between our analytical and numerical results.",
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The stability of obliquely-propagating solitary-wave solutions to Zakharov-Kuznetsov-type equations. / Parkes, E.J.; Munro, S.

In: Journal of Plasma Physics, Vol. 71, No. 5, 10.2005, p. 695-708.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The stability of obliquely-propagating solitary-wave solutions to Zakharov-Kuznetsov-type equations

AU - Parkes, E.J.

AU - Munro, S.

PY - 2005/10

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N2 - In certain circumstances, small amplitude, weakly nonlinear ion-acoustic waves in a magnetized plasma are governed by a Zakharov-Kuznetsov equation or by a reduced form of the equation. Both equations have a plane solitary travelling-wave solution that propagates at an angle αto the magnetic field. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the initial growth rate of a small, transverse, long-wavelength perturbation to these solitary-wave solutions. Previous results in the literature are corrected. A numerical determination of the growth rate is given. For k[mid R:] secα[mid R:][double less-than sign]1, where k is the wavenumber of the perturbation, there is excellent agreement between our analytical and numerical results.

AB - In certain circumstances, small amplitude, weakly nonlinear ion-acoustic waves in a magnetized plasma are governed by a Zakharov-Kuznetsov equation or by a reduced form of the equation. Both equations have a plane solitary travelling-wave solution that propagates at an angle αto the magnetic field. The multiple-scale perturbation method developed by Allen and Rowlands is used to calculate the initial growth rate of a small, transverse, long-wavelength perturbation to these solitary-wave solutions. Previous results in the literature are corrected. A numerical determination of the growth rate is given. For k[mid R:] secα[mid R:][double less-than sign]1, where k is the wavenumber of the perturbation, there is excellent agreement between our analytical and numerical results.

KW - solitary-wave solutions

KW - equations

KW - plasma physics

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