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Abstract
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.
Acknowledgements
Research support from, Ministry of Minority Affairs through UGC, Government of India (Ref. /
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) 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. The authors would like to thank anonymous referees for their helpful comments and suggestions on earlier version of this article.