Lie transformation group solutions of the nonlinear one-dimensional Vlasov equation
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), Vol. 26:6
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN-VLASOV EQUATION
ANALYTICAL SOLUTION
TRANSFORMATIONS
PLASMA WAVES
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRIC FIELDS
INTEGRAL EQUATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
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