Details

Autor(en) / Beteiligte

• MUNRO, S.
• PARKES, E. J.

Titel

Stability of solitary-wave solutions to a modified Zakharov–Kuznetsov equation

Ist Teil von

• Journal of plasma physics, 2000-10, Vol.64 (4), p.411-426

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2000

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In the context of ion-acoustic waves in a magnetized plasma comprising cold ions and non-isothermal electrons, small-amplitude, weakly nonlinear waves have been shown previously by Munro and Parkes to be governed by a modified version of the Zakharov–Kuznetsov equation. In this paper, we consider solitary travelling-wave solutions to this equation that propagate along the magnetic field. We investigate the initial growth rate γ(k) of a small transverse sinusoidal perturbation of wavenumber k. The instability range is shown to be 0 < k < 3. We use the multiple-scale perturbation method developed by Allen and Rowlands to determine a consistent expansion of γ about k = 0 and k = 3. By combining these results in the form of a Padé approximant, an analytical expression for γ is found that is valid for 0 < k < 3. γ is also determined by using the variational method developed by Bettinson and Rowlands. The two results for γ are compared with a numerical determination.