Symmetry analysis, invariant subspace and conservation laws of the equation for fluid flow in porous media

Author:

Yusuf Abdullahi12ORCID

Affiliation:

1. Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey

2. Department of Mathematics, Federal University Dutse, Jigawa 7156, Nigeria

Abstract

The equation for fluid flow in porous media is analyzed in this paper with the aid of Lie symmetry method (LSM) and invariant subspace method (ISM). Infinitesimal generators, the entire geometric fields of the vectors and the symmetry groups of the equation being considered are given. One-dimensional optimal systems of sub-algebra are reported with corresponding reduced nonlinear ordinary differential equations. By means of ISM, we determine the exact solutions and invariant subspaces (ISs) for the equation under consideration. Moreover, with the aid of the new theorem of conservation, we establish the conservation laws (CLs) for the governing equation. The construction of the conserved vectors reveals the integrability and existence of soliton solutions of the equation for fluid flow in porous media.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

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