(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, the (2 + 1)-dimensional Lin–Reissner–Tsien (LRT) equation is investigated using the Power Index Method (PIM). A self-similar transformation is applied to reduce the given partial differential equation (PDE) into an ordinary differential equation (ODE) through a change of variables based on scaling symmetry. The analytic solution of the resulting ODE is obtained using the symbolic computation software Maple 18 and basic techniques. The self-similar solutions of the LRT equation are then derived by combining the ODE solution with the self-similar transformation. The proposed method is effectively applied to generate new self-similar solutions of the LRT equation. Finally, graphical representations of all the obtained solutions are presented as 3D plots generated using Maple 18.