Optimal System and Symmetry reductions of the Vibrating Plate Equation

In this paper, An optimal system of one-dimensional subalgebras is constructed for the nonlinear vibrating plate equation, and symmetry reductions together with group-invariant solutions are derived. The results provide new insight into the solution structure of the vibrating plate equation and may serve as a foundation for further analysis of related nonlinear models.

Keywords:

optimal system , vibrating plate equation , symmetry reductions , invariant solutions