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Stability of an alternative solitary-wave solution of an ion-acoustic wave obtained from the MKdV–KdV–ZK equation in magnetized non-thermal plasma consisting of warm adiabatic ions

  • JAYASREE DAS (a1), ANUP BANDYOPADHYAY (a2) and K. P. DAS (a3)

Abstract

The Korteweg–de Varies–Zakharov–Kuznetsov (KdV–ZK) equation describes the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external magnetic field in a non-thermal plasma consisting of warm adiabatic ions. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion-acoustic wave is described by a modified KdV–ZK (MKdV–ZK) equation. A combined MKdV–KdV–ZK equation more efficiently describes the nonlinear behaviour of ion-acoustic waves at points in the neighbourhood of the curve in the parametric plane along which the coefficient of the nonlinear term of the KdV–ZK equation vanishes. This combined MKdV–KdV–ZK equation admits both double-layer and alternative solitary-wave solutions having profile different from sech$^{2}$ or sech. In this paper the three-dimensional stability of the alternative solitary-wave solution having profile different from sech$^{2}$ or sech has been investigated by the recently developed multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of instability have been derived at the lowest order. The correct expression of the growth rate of instability at the lowest order has been obtained for a limiting case and the stability analysis has been carried out numerically from our model as presented in this paper for arbitrary values of the parameters involved in the system.

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