ASYMPTOTIC SYMMETRIES AND ASYMPTOTICALLY SYMMETRICAL SOLUTIONS OF PARTIAL-DIFFERENTIAL EQUATIONS

Symmetry methods for differential equations are a powerful tool to att ack nonlinear problems, in particular for determining solutions with g iven symmetries to nonlinear PDES. Since in real applications one is o ften interested in solutions which are asymptotically symmetric, we pr opose here an approach to asymptotic symmetry based on the methods of Lie theory. We adopt, translate in geometric language and develop the renormalization group approach recently proposed by Bricmont and Kupia inen for the Ginzburg-Landau equation.