| Finding solutions of nonlinear partial differential equations, either exact or analytical, is one of the challenging problems in applied mathematics. In particular, the case of higher-order systems of nonlinear partial differential equations poses the most difficult challenge. Lie symmetry method provides a powerful tool for the generation of transformations that can be used to transform the given differential equation to a simpler equation while preserving the invariance of the original equation. Consequently, it enjoys a widespread application and has attracted the attention of many researchers.; In this research work a complete classification of a family of nonlinear (1+2)-dimensional wave equations, in which the nonlinearity is introduced through a function representing the wave speed, has been done. All possible symmetries of this wave equation are derived and a set of reductions to ordinary differential equations under two-dimensional sub-algebras is given. |
