Extended symmetries of the 3D kinetic electron plasma waves

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Extended symmetries of the 3D kinetic electron
plasma waves   

• V. B. Taranov
• Institute for Nuclear Research, Kyiv, Ukraine
• v.taranov_at_hotmail.com

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Manifold of solutions

• Lie point, conditional and extended symmetries

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A
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B
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C
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D
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E
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MAPLE 12 PROGRAM
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Mexican hat
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CONCLUSIONS

• 1. Hydrodynamic plasma theory.
• Continuous symmetries of the partial differential
  equations can be obtained by usual Lie group
  algorithm. Standard programs of Maple 12 package
  allow us to find the symmetries for nonlinear
  equations and systems of equations.
• Conditional symmetries are possible when the
  manifold of solutions is reduced by certain
  additional conditions. From the physical point of
  view, these symmetry extensions are due to the
  simpler structure of nonlinear waves in the
  vicinity of their critical points.
• 2. Kinetic plasma theory.
• Continuous symmetries of the integro-differential
  equations can be obtained by an indirect method
  (from the symmetries of the infinite system of
  PDEs for the moments of distribution functions)
  and by the direct methods. Maple 12 standard
  programs can help us even in this case.
• Conditional symmetries are possible in kinetic
  theory case, too.
• Moreover, extended symmetries appear if some
  global conditions are weakened.
• Wavelet type extended symmetries are possible
  for the systems containing finite order moments
  of distribution functions.

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