Special Session 45: Lie Symmetries, Conservation Laws and Other Approaches in Solving Nonlinear Differential Equations

A study of a generalized nonlinear advection-diffusion equation

Chaudry Masood Khalique
North-West University
So Africa
Co-Author(s):    
Abstract:
In this talk, we investigate a nonlinear partial differential equation of fluid mechanics, namely, the generalized nonlinear advection-diffusion equation, which describes the movement of a buoyancy-driven plume in an inclined porous medium. We shall consider three cases of n and in each case, we shall provide symmetry reductions and group-invariant solutions based on the optimal systems of one-dimensional subalgebras. Furthermore, we determine the conserved vectors by employing the multiplier approach.