Lie group analysis and exact solutions of nonlinear dispersive equations for porous media

Dispersive equations have recently been attractive in the nonlinear wave phenomena appearing in many applications of science and engineering. In this work, the symmetry solutions of the dispersive equation with porous medium-type nonlinearity, which is a generalized nonlinear dispersion-diffusion model, are revealed. To obtain the exact solutions of nonlinear equations, various techniques, including the ansatz methods, are applied in the literature. This work uses the classical Lie group of transformations, which is the most general and effective one. The long-time behaviour of solutions is discussed regarding the different powers of nonlinearities.