Group Analysis and Exact Solutions of the Dynamic Equations of Plane Strain of an Incompressible Nonlinearly Elastic Body

Under study is the plane strain dynamics of an incompressible body in the framework of a nonlinear model of elasticity which uses the actual state variables. We obtain some system of nonlinear equations for displacement and pressure, give the exact solutions of the equations by using group analysis, and indicate the area of the possible application of these solutions.