Group invariant solutions of (2+1)-dimensional rdDym equation using optimal system of Lie subalgebra

We use the Lie group method to investigate a one-dimensional optimal system of Lie subalgebra for a (2+1)-dimensional rdDym equation. The new closed form solutions of the rdDym equation are constructed. The rdDym equation has been changed into a new partial differential equation which has fewer independent variables. To explain the physical significance of invariant solutions, 3D, 2D and contour plots are exploited by numerical simulation. Some of the results are new as compared with previously established outcomes (Baran et al 2016 Theor. Math. Phys. 188 1273–1295; Morozov 2012 SIGMA 8 051; Lelito and Morozov 2018 J. Geom. Phys. 131 89–100). Interestingly, one lump-type solution, kink waves and a parabolic profile of the group invariant solutions are shown to make this research more valuable.