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

Y1 - 2005/10

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

UR - http://www.maths.strath.ac.uk/~caas35/p&mJPP05.pdf

UR - http://dx.doi.org/10.1017/S0022377805003727

U2 - 10.1017/S0022377805003727

DO - 10.1017/S0022377805003727

M3 - Article

VL - 71

SP - 695

EP - 708

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

SN - 0022-3778

IS - 5

ER -