Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation

Journal Article · Sat Jun 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526964· OSTI ID:5882920

Abraham-Shrauner, B

The solution of the exact, nonlinear one-dimensional Vlasov equation with a space- and time-dependent electric field is reduced to the solution of a nonlinear, first-order ordinary differential equation with two subsidiary equations. The reduction holds for any electric field nonlinear in the spatial coordinate or for a subclass of electric fields linear in the spatial coordinate and is equivalent to the solution of a generalized Bernstein--Greene--Kruskal (BGK) Vlasov equation with a velocity-dependent Lorentz force. The Lie method for the solution of differential equations invariant under a transformation group has been used to calculate the group generator, the canonical variables, and the generalized BGK Vlasov equation. Analytical forms for the functional dependence of the Vlasov equation one-particle distribution function are given.

• Research Organization: Department of Electrical Engineering, Washington University, St. Louis, Missouri 63130
• OSTI ID: 5882920
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700108* -- Fusion Energy-- Plasma Research-- Wave Phenomena
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
INTEGRAL EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA WAVES
SYMMETRY GROUPS
TIME DEPENDENCE
TRANSFORMATIONS