Institute for Nuclear Research,

47 Nauky Ave.,

Kyiv 03028,

UKRAINE

E-mail: vebete@yahoo.com

**Extended symmetries of the kinetic plasma theory models**

**Abstract:**

Extended symmetries of the kinetic plasma theory models. Abstract:
In recent decades the Lie group method has been applied to explore many
physically interesting

nonlinear problems in gas dynamics, plasma physics etc. Furthermore,
extensions of the classical Lie algorithm to the integro-differential systems
of equations of kinetic theory were proposed. It was shown that Lie symmetry
group of the integro-differential equations of kinetic plasma theory is
larger than that of its hydrodynamic approximations based on the partial
differential equations. For the collisionless plasmas containing components
with equal charge to mass ratio of particles, this result was first obtained
by an indirect algorithm which allows us to built symmetries of the integro-differential
kinetic equations via the symmetries of an infinite set of partial differential
equations for the moments of distribution functions. Even more large symmetries
were obtained by explicit symmetry exploration methods working directly
with integro-differential equations of the kinetic models. Unfortunately,
these additional symmetry extensions are incompatible with the existence
of charge and current density integrals present in Maxwell field equations.
It must be noted that the above mentioned indirect algorithm is free of
these incompatibility problems.