DETERMINATION OF THE GROWTH-RATE FOR THE LINEARIZED ZAKHAROV-KUZNETSOV EQUATION

被引:78
作者
ALLEN, MA
ROWLANDS, G
机构
[1] Department of Physics, University of Warwick, Coventry
关键词
D O I
10.1017/S0022377800017244
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Studies of the Zakharov-Kuznetsov equation governing solitons in a strongly magnetized ion-acoustic plasma indicate that a perturbed flat soliton is unstable and evolves into higher-dimensional solitons. The growth rate gamma = gamma(k) of a small sinusoidal perturbation of wavenumber k to a flat soliton has already been found numerically, and lengthy analytical work has given the value of dgamma/dk at k = 0. We introduce a more direct analytical method in the form of an extension to the usual multiple-scale perturbation approach and use it to determine a consistent expansion of gamma about k = 0 and the other zero at k2 = 5. By combining these results in the form of a two-point Pade approximant, we obtain an analytical expression for gamma valid over the entire range of k for which the solution is unstable. We also present a very efficient numerical method for determining the growth rate curve to great accuracy. The Pade approximant gives excellent agreement with the numerical results.
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页码:413 / 424
页数:12
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