Solutions and reductions for radiative energy transport in laser-heated plasma

A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential symmetries and to an integrable nonlinear model. Classical poi...

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Bibliographic Details
Published in:Journal of mathematical physics 2015-01, Vol.56 (1), p.1
Main Authors: Broadbridge, P, Ivanova, N M
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CONSERVATION LAWS
Energy conservation
Energy transfer
EXACT SOLUTIONS
Laser beam heating
LASERS
Mathematical models
Mathematical problems
Nonlinear equations
NONLINEAR PROBLEMS
Physics
PLASMA
Plasma physics
REDUCTION
SYMMETRY
TIME DEPENDENCE
Transport
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Summary:A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential symmetries and to an integrable nonlinear model. Classical point symmetries, potential symmetries, and nonclassical symmetries are used to effect variable reductions and exact solutions. The simplest time-dependent solution is shown to be stable and relevant to a closed system.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4905646