Symmetry analysis and invariant solutions of Riabouchinsky Proudman Johnson equation using optimal system of Lie subalgebras

Abstract

The Lie symmetry analysis of the Riabouchinsky Proudman Johnson (RPJ) equation is discussed in this research. In the onset, we derive the geometric vector fields using the classical Lie symmetry technique. Here, we have a four-dimensional Lie algebra. A five-dimensional optimal system is then obtained utilising this four-dimensional Lie algebra. After that, due to the similarity reduction, nonlinear ordinary differential equations (ODEs) are obtained. These nonlinear ODEs are very significant to reveal the dynamical profile of the solution regions of the RPJ equation. The obtained solutions have applications in fluid dynamics and are helpful for recent research because they are associated to Reynolds numbers. For the purpose of understanding the physical significance of the identified solutions, Mathematica simulations of those solutions are also provided.