Analysis of the von Kármán equations by group methods (Q1062809)

One of the systems of equations approximating the large deflection of plates consists of two coupled nonlinear fourth order partial differential equations, known as the von Kármán equations. The full symmetry group for the steady equations is a finitely generated Lie group with ten parameters. For the time-dependent system the full symmetry group is an infinite parameter Lie group. Several subgroups of the full group are used to generate exact solutions of the time-independent and the time-dependent systems. These include the dilatation group (similar solutions), rotation group, screw group and others. Physical implications and applications are discussed.