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The derivation of a modified Zakharov–Kuznetsov equation and the stability of its solutions

  • S. MUNRO (a1) and E. J. PARKES (a1)
  • Published online: 01 September 1999

The Zakharov-Kuznetsov equation governs the behaviour of weakly non-linear 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.

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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
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