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Asymptotic symmetries and asymptotically symmetric solutions of partial differential equations. (English) Zbl 0821.35127
Summary: Symmetry methods for differential equations are a powerful tool to attack nonlinear problems, in particular for determining solutions with given symmetries to nonlinear PDEs. Since in real applications one is often interested in solutions which are asymptotically symmetric, we propose here an approach to asymptotic symmetry on the methods of Lie theory. We adopt, translate in geometric language and develop the renormalization group approach recently proposed by Bricmont and Kupiainen for the Ginzburg-Landau equation.

MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
58J72Correspondences and other transformation methods (PDE on manifolds)
81T17Renormalization group methods (quantum theory)