Invariant solutions of integro-differential Vlasov–Maxwell equations in Lagrangian variables by Lie group analysis

Rezvan, Farshad; Özer, Teoman

doi:10.1016/j.camwa.2010.03.029

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Kovalev [9] applied Lie group technique for studying nonlinear multi-scale systems. Lie algebra of point symmetries and invariant solutions of the integro-partial differential Vlasov-Maxwell system in Lagrangian variables is analyzed by Rezvan and Ozer [10]. Sahin et al [11] investigated the selfsimilarity solutions of the one-layer shallow-water equations representing gravity currents using Lie group analysis.…”

Section: Introductionmentioning

confidence: 99%

Lie group analysis and propagation of weak discontinuity in one-dimensional ideal isentropic magnetogasdynamics

Bira

Sekhar

2014

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The aim of this paper is to carry out symmetry group analysis to obtain important classes of exact solutions from the given system of nonlinear partial differential equations (PDEs). Lie group analysis is employed to derive some exact solutions of one dimensional unsteady flow of an ideal isentropic, inviscid and perfectly conducting compressible fluid, subject to a transverse magnetic field for the magnetogasdynamics system. By using Lie group theory, the full one-parameter infinitesimal transformations group leaving the equations of motion invariant is derived. The symmetry generators are used for constructing similarity variables which leads the system of PDEs to a reduced system of ordinary differential equations; in some cases, it is possible to solve these equations exactly. Further, using the exact solution, we discuss the evolutionary behavior of weak discontinuity.

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Section: Introductionmentioning

confidence: 99%