Lie group analysis and its invariants for the class of multidimensional nonlinear wave equations

We systematically classify Lie symmetries of a class of (2 + 1)-dimensional nonlinear wave equations. Our methodology proposes a symmetry classification for Lie generators applicable to four distinct cases inherent within this equation. For each identified category, we comprehensively analyze symmetry reduction and delineate the invariant solutions. Furthermore, we extend our Lie symmetry analysis to encompass reduced 1 + 1 partial differential equations (PDEs). Through our investigations, we establish local conservation laws corresponding to each conserved vector, employing the formal Lagrangian approach. Significantly, this classification constitutes a novel contribution to the scientific discourse, as it remains absent from extant literature to date.