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Exact solutions to magnetogasdynamic equations in Lagrangian coordinates

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Abstract

The Lie group of point transformations, which leave the equations for a simplified model of one dimensional ideal gas in magnetogasdynamics invariant, are used to obtain some exact solutions for the governing system of hyperbolic partial differential equations (PDEs). Similarity variables which reduces the governing system of PDEs into system of ordinary differential equations (ODEs) are determined through the transformations. The resulting ODEs are solved analytically to obtain some exact solutions that exhibits space-time dependence. Further, we study the propagation of weak discontinuity through a state characterized by one of the solutions.

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Acknowledgments

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) are gratefully acknowledged by the first and second authors, respectively.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Science and Technology, Palur Hills, Berhampur, 761008, India

    B. Bira

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    T. Raja Sekhar

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  1. B. Bira
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  2. T. Raja Sekhar
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Correspondence to T. Raja Sekhar.

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Bira, B., Raja Sekhar, T. Exact solutions to magnetogasdynamic equations in Lagrangian coordinates. J Math Chem 53, 1162–1171 (2015). https://doi.org/10.1007/s10910-015-0476-8

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  • DOI: https://doi.org/10.1007/s10910-015-0476-8

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