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

DOI10.1063/1.526964zbMath0611.76129OpenAlexW2092551568WikidataQ115332200 ScholiaQ115332200MaRDI QIDQ3751305

Barbara Abraham-Shrauner

Publication date: 1985

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.526964

zbMATH Keywords

electric fieldLie groupcharacteristic equationLie group methodcomplete solutioninfinitesimal transformationplasma kinetic theoryexact, nonlinear, one-dimensional Vlasov equationgeneralized BGK distribution functiongeneralized BGK Vlasov equationLiouville invariant

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Statistical mechanics of plasmas (82D10) Partial differential equations of mathematical physics and other areas of application (35Q99) Ionized gas flow in electromagnetic fields; plasmic flow (76X05)

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An alternate approach to finding and using the Lie group of the Vlasov equation, Lie group symmetries and invariants of the Hénon–Heiles equations, The formation of nonuniform structures in charged-particle beams

Cites Work

• Exact Nonlinear Plasma Oscillations
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• Exact, time-dependent solutions of the one-dimensional Vlasov–Maxwell equations
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• Exact, Stationary Wave Solutions of the Nonlinear Vlasov Equation