On the symmetry group properties of equations of nonlocal elasticity

Abstract

The author finds symmetry groups for one-dimensional and two-dimensional equations of nonlocal elasticity in dynamic problems. At first, the determining equations are derived together with differential equations which include kernel functions. Then, using these functions and solving the determining equations, the author obtains symmetry groups and gives their classification with respect to kernel functions. The results presented in this paper can be used as a preliminary tool in order to investigate solutions and symmetry groups of nonlocal elasticity. A special application is possible to solutions of boundary value problems in nonlocal elasticity when the classical solutions are singular.