Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 006, 7 pages      arXiv:0801.2773      https://doi.org/10.3842/SIGMA.2008.006
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Symmetry Extensions and Their Physical Reasons in the Kinetic and Hydrodynamic Plasma Models

Volodymyr B. Taranov
Institute for Nuclear Research, 47 Nauky Ave., 03028 Kyiv, Ukraine

Received October 31, 2007, in final form January 14, 2008; Published online January 17, 2008

Abstract
Characteristic examples of continuous symmetries in hydrodynamic plasma theory (partial differential equations) and in kinetic Vlasov-Maxwell models (integro-differential equations) are considered. Possible symmetry extensions conditional and extended symmetries are discussed. Physical reasons for these symmetry extensions are clarified.

Key words: symmetry; plasma; hydrodynamic; kinetic.

pdf (166 kb)   ps (124 kb)   tex (9 kb)

References

  1. Ibragimov N.H., Kovalev V.F., Pustovalov V.V., Symmetries of integro-differential equations: a survey of methods illustrated by the Benney equation, Nonlinear Dynam. 28 (2002), 135-165, math-ph/0109012.
  2. Cicogna G., Ceccherini F., Pegoraro F., Applications of symmetry methods to the theory of plasma physics, SIGMA 2 (2006), 017, 17 pages, math-ph/0602008.
  3. Taranov V.B., On the symmetry of one-dimensional high frequency motions of a collisionless plasma, Sov. J. Tech. Phys. 21 (1976), 720-726.
  4. Gordeev A.V., Kingsep A.S., Rudakov L.I., Electron magnetohydrodynamics, Phys. Rep. 243 (1994), 215-465.
  5. Meleshko S.V., Application of group analysis in gas kinetics, in Proc. Joint ISAMM/FRD Inter-Disciplinary Workshop "Symmetry Analysis and Mathematical Modelling", 1998, 45-60.
  6. Horton W., Drift waves and transport, Rev. Modern Phys. 71 (1999), 735-778.
  7. Taranov V.B., Drift and ion-acoustic waves in magnetized plasmas, symmetries and invariant solutions, Ukrainian J. Phys. 49 (2004), 870-874.
  8. Taranov V.B., Symmetry extensions in kinetic and hydrodynamic plasma models, in Proceedinds of 13th International Congress on Plasma Physics (2006, Kyiv), 2006, A041p, 4 pages.
  9. Cicogna G., Laino M., On the notion of conditional symmetry of differential equations, Rev. Math. Phys. 18 (2006), 1-18, math-ph/0603021.

Previous article   Next article   Contents of Volume 4 (2008)