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On Lie symmetry analysis of nonhomogeneous generalized inviscid and fractional Burgers' equation
Author(s) -
Saqib Muhammad,
Hussain Qamar,
Hamid Kara Abdul,
Zaman Fiazuddin
Publication year - 2021
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.7300
Subject(s) - inviscid flow , burgers' equation , mathematics , homogeneous space , mathematical analysis , symmetry (geometry) , partial differential equation , mathematical physics , classical mechanics , physics , geometry
Nonhomogeneous inviscid Burgers' equation arises in one‐dimensional inviscid flow in the presence of external force. Inter alia, its applications are in optics: nonlinear fibre and geometrical, for example. We study a generalized form of this equation from Lie symmetry stand point. Reductions and invariant solutions are presented using the similarity variables thus obtained. To account for modeling of diffusion process by fractional time derivative, Lie symmetries and reduction of time‐fractional inviscid Burgers' equation are also presented.