PIMS-IAM Distinguished Colloquium: Vladimir Dorodnitsyn

A group classification of first-order and second-order delay ordinary differential equations is presented. A delay ordinary differential system (DODS) is a delay ordinary differential equation (DODE) accompanied by a delay relation, i.e. an equation which describes a delay parameter. Linear DODSs which consists of a linear DODEs and solution independent delay relations have infinite-dimensional symmetry algebras as do nonlinear ones which are linearizable by an invertible transformation of variables. In general nonlinear DODS have symmetry algebras of dimension 0 n 3. It is shown how exact analytical solutions of invariant DODS can be obtained by means of a symmetry reduction.