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Symmetry analysis and optimal systems of generalized Chaplygin gas equations with a source term
Author(s) -
Pradhan Pabitra Kumar,
Pandey Manoj Kumar
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6348
Subject(s) - chaplygin gas , mathematics , invariant (physics) , discontinuity (linguistics) , term (time) , symmetry (geometry) , transformation (genetics) , lie group , symmetry group , mathematical analysis , mathematical physics , pure mathematics , geometry , physics , quantum mechanics , dark energy , cosmology , biochemistry , chemistry , gene
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.