Lie Symmetry Analysis and Explicit Solutions to the Estevez–Mansfield–Clarkson Equation

In this study, we investigate the symmetry analysis and explicit solutions for the Estevez–Mansfield–Clarkson (EMC) equation. Our main objectives are to identify the Lie point symmetries of the EMC equation, construct an optimal system of one-dimensional subalgebras, and reduce the EMC equation to a set of ordinary differential equations (ODEs). We employ the Riccati–Bernoulli sub-ODE method (RBSODE) to solve these reduced ODEs and obtain explicit solutions for the EMC model. The obtained solutions are validated using numerical analyses, and corresponding figures are presented to illustrate the physical implications of the derived solutions.