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STABILITY OF OBLIQUELY PROPAGATING PLANE SOLITONS OF THE ZAKHAROV-KUZNETSOV EQUATION
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UNSPECIFIED (1995) STABILITY OF OBLIQUELY PROPAGATING PLANE SOLITONS OF THE ZAKHAROV-KUZNETSOV EQUATION. JOURNAL OF PLASMA PHYSICS, 53 (Part 1). pp. 63-73. ISSN 0022-3778.
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Abstract
By determining to first order the growth rate of a small, long-wavelength, perturbation to a Zakharov-Kuznetsov plane soliton moving at an angle alpha to the magnetic field, it has been found that such solitons are unstable for alpha < alpha(0) (approximate to 38 degrees). To determine the stability for angles greater than alpha(0) one needs the growth rate to higher order. The conventional approach generates a second-order growth rate that is singular at alpha = alpha(0). We rigorously obtain an expression that is bounded at this point, by developing a method in which exponentially secular terms that arise are regrouped before their subsequent elimination. We then show that these solitons are unstable for all alpha, although the growth rate is small for alpha > alpha(0) and goes to zero as alpha --> 1/2 pi. The relevant linearized equation is solved numerically, and excellent agreement between analytical and numerical results is obtained.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Journal or Publication Title: | JOURNAL OF PLASMA PHYSICS | ||||
Publisher: | CAMBRIDGE UNIV PRESS | ||||
ISSN: | 0022-3778 | ||||
Official Date: | February 1995 | ||||
Dates: |
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Volume: | 53 | ||||
Number: | Part 1 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 63-73 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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