On Lie symmetry analysis of nonhomogeneous generalized inviscid and fractional Burgers' equation

摘要

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.