TY - JOUR

T1 - Stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation

AU - Munro, S.

AU - Parkes, E.J.

PY - 2000/10

Y1 - 2000/10

N2 - In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, small-amplitude, weakly nonlinear waves have been shown previously by Munro and Parkes to be governed by a modified version of the Zakharov-Kuznetsov equation. In this paper, we consider solitary travelling-wave solutions to this equation that propagate along the magnetic field. We investigate the initial growth rate [gamma](k) of a small transverse sinusoidal perturbation of wavenumber k. The instability range is shown to be 0 < k < 3. We use the multiple-scale perturbation method developed by Allen and Rowlands to determine a consistent expansion of [gamma] about k = 0 and k = 3. By combining these results in the form of a Padæ#169; approximant, an analytical expression for [gamma] is found that is valid for 0 < k < 3. [gamma] is also determined by using the variational method developed by Bettinson and Rowlands. The two results for [gamma] are compared with a numerical determination.

AB - In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, small-amplitude, weakly nonlinear waves have been shown previously by Munro and Parkes to be governed by a modified version of the Zakharov-Kuznetsov equation. In this paper, we consider solitary travelling-wave solutions to this equation that propagate along the magnetic field. We investigate the initial growth rate [gamma](k) of a small transverse sinusoidal perturbation of wavenumber k. The instability range is shown to be 0 < k < 3. We use the multiple-scale perturbation method developed by Allen and Rowlands to determine a consistent expansion of [gamma] about k = 0 and k = 3. By combining these results in the form of a Padæ#169; approximant, an analytical expression for [gamma] is found that is valid for 0 < k < 3. [gamma] is also determined by using the variational method developed by Bettinson and Rowlands. The two results for [gamma] are compared with a numerical determination.

UR - http://www.maths.strath.ac.uk/~caas35/m&pJPP00.pdf

UR - http://journals.cambridge.org/action/displayFulltext?type=1&fid=76266&jid=&volumeId=&issueId=04&aid=76265

M3 - Article

VL - 64

SP - 411

EP - 426

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

IS - 4

ER -