The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions
The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions
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DOI：
10.1017/s0022377899007874
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发表时间：
1999-09-01
影响因子：
2.5
通讯作者：
Parkes, EJ
中科院分区：
文献类型：
--
作者：
Munro, S;Parkes, EJ
Zakharov-Kuznetsov方程描述了在均匀磁场中等离子体中弱非线性离子声波的行为。我们考虑更现实的情况下，电子是非等温的。通过对Schamel提出的电子数密度的适当修正，我们证明了约化微扰过程导致了修正的Zakharov-Kuznetsov（mZK）方程.利用Rowlands和Infeld的方法研究了mZK方程的平面周期和孤立行波解对二维长波扰动的稳定性.
The Zakharov-Kuznetsov equation governs the behaviour of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. We consider the more realistic situation in which the electrons are non-isothermal. With an appropriate modified form of the electron number density proposed by Schamel, we show that the reductive perturbation procedure leads to a modified Zakharov-Kuznetsov (mZK) equation. The stability of plane-periodic and solitary travelling-wave solutions of the mZK equation to two-dimensional long-wavelength perturbations is investigated using the method of Rowlands and Infeld.