, Volume 48, Issue 5, pp 1023–1029 | Cite as

Exact solutions to magnetogasdynamics using Lie point symmetries

  • B. Bira
  • T. Raja Sekhar


In the present work, we find some exact solutions to the first order quasilinear hyperbolic system of partial differential equations (PDEs), governing the one dimensional unsteady flow of inviscid and perfectly conducting compressible fluid, subjected to a transverse magnetic field. For this, Lie group analysis is used to identify a finite number of generators that leave the given system of PDEs invariant. Out of these generators, two commuting generators are constructed involving some arbitrary constants. With the help of canonical variables associated with these two generators, the assigned system of PDEs is reduced to an autonomous system whose simple solutions provide nontrivial solutions of the original system. Using this exact solution, we discuss the evolutionary behavior of weak discontinuities.


Magnetogasdynamics Group theoretic method Hyperbolic system Exact solution Weak discontinuities 



Research support from, Ministry of Minority Affairs through UGC, Government of India (Ref. F1-17.1/2010/MANF-CHR-ORI-1839/(SA-III/Website)) and National Board for Higher Mathematics, Department of Atomic Energy, Government of India (Ref. No. 2/48(1)/2011/-R&D II/4715), gratefully acknowledged by the first and second authors, respectively.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of Technology RourkelaRourkela-8India

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