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Zbl 0821.35127
Gaeta, Giuseppe
Asymptotic symmetries and asymptotically symmetric solutions of partial differential equations. (English)
[J] J. Phys. A, Math. Gen. 27, No.2, 437-451 (1994). ISSN 0305-4470

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 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
58J72 Correspondences and other transformation methods
81T17 Renormalization group methods

Keywords: asymptotic symmetry; Lie theory; renormalization group approach; Ginzburg-Landau equation

Cited in: Zbl 1093.35004

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	Scientific prize winners of the ICM 2010
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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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Zentralblatt MATH Berlin [Germany]