Symmetry analysis and optimal systems of generalized Chaplygin gas equations with a source term |
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Authors: | Pabitra Kumar Pradhan Manoj Kumar Pandey |
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Affiliation: | Department of Mathematics, Birla Institute of Technology and Science Pilani K K Birla Goa Campus, Pilani, Goa, India |
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Abstract: | The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one- and two-dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one-dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour. |
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Keywords: | Lie symmetries first - order hyperbolic systems Chaplygin gas equations weak discontinuities |
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