Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T14:46:09.206Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas

Published online by Cambridge University Press:  08 November 2016

Piotr Goldstein  and
Eryk Infeld
Piotr Goldstein*
Affiliation:
Theoretical Physics Division, National Centre for Nuclear Research, Hoża 69, 00-681 Warsaw, Poland
Eryk Infeld
Affiliation:
Theoretical Physics Division, National Centre for Nuclear Research, Hoża 69, 00-681 Warsaw, Poland
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special cases. A historical overview of the problem concludes the paper.

Keywords

magnetized plasmasplasma nonlinear phenomenaplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 6 , December 2016 , 905820603
Copyright
© Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, M. J. & Rowlands, G. 1993 Determination of the growth rate for the linearized Zahkarov–Kuznetsov equation. J. Plasma Phys. 50, 413–424.CrossRefGoogle Scholar
Allen, M. J. & Rowlands, G. 1995 Stability of obliquely propagating plane solitons of the Zakharov–Kuznetsov equation. J. Plasma Phys. 53, 63–73.CrossRefGoogle Scholar
Allen, M. J. & Rowlands, G. 1997 On the transverse instabilities of solitary waves. Phys. Lett. A 235, 145–146.CrossRefGoogle Scholar
Bas, E. & Bulent, K. 2010 New complex solutions for Rlw Burgers equation, generalized Zakharov–Kuznetsov equation and coupled Korteweg–De Vries equation. World Appl. Sci. J. 11, 256–262.Google Scholar
Infeld, E. 1985 Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. J. Plasma Phys. 33, 171–182.CrossRefGoogle Scholar
Infeld, E. & Frycz, P. 1987 Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. Part 2. Numerical simulations, two-soliton collisions. J. Plasma Phys. 37, 97–106.CrossRefGoogle Scholar
Infeld, E. & Frycz, P. 1989 Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. Part 3. Arbitrary-angle perturbations, period doubling of waves. J. Plasma Phys. 41, 441–446.Google Scholar
Infeld, E. & Rowlands, G. 1977 Stability of solitons to transverse perturbations. J. Plasma Phys. 19, 343–348.CrossRefGoogle Scholar
Infeld, E. & Rowlands, G. 2000 Nonlinear Waves, Solitons and Chaos, 2nd edn, chap. 8. Cambridge University Press.CrossRefGoogle Scholar
Laedke, W. & Spatchek, K. H. 1982 Growth rates of bending KdV solitons. J. Plasma Phys. 28, 469–484.CrossRefGoogle Scholar
Mothibi, D. M. & Khalique, C. M. 2015 Conservation laws and exact solutions of a generalized Zakharov–Kuznetsov equation. Symmetry 7, 949–961.CrossRefGoogle Scholar
Munro, S. & Parkes, E. J. 1999 The derivation of a modified Zakharov–Kuznetsov equation and the stability of its solutions. J. Plasma Phys. 62, 305–317.CrossRefGoogle Scholar
Murawski, K. & Edwin, P. M. 1992 The Zakharov–Kuznetsov equation for nonlinear ion-acoustic waves. J. Plasma Phys. 47, 75–83.CrossRefGoogle Scholar
Nawaz, T., Yildirim, A & Mohyud-Din, S. T. 2013 Analytical solutions Zakharov–Kuznetsov equations. Adv. Powder Technol. 24, 252–256.CrossRefGoogle Scholar
Zakharov, V. E. & Kuznetsov, E. A. 1974 On three dimensional solitons. Zh. Eksp. Teor. Fiz. 66, 594–597; Sov. Phys. JETP 39, 285–286.Google Scholar