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Effective integrable
dynamics for a certain nonlinear wave equation
Patrick Gérard and Sandrine Grellier |
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Vol. 5 (2012), No. 5, 1139–1155
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Abstract |
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We consider the following degenerate half-wave equation on the one-dimensional torus: We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system—the cubic Szegő equation. As a consequence, we prove an instability result for large norms of solutions of this wave equation. |
Keywords
Birkhoff normal form, nonlinear wave equation, perturbation
of integrable systems
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Mathematical Subject Classification 2010
Primary: 35B34, 35B40, 37K55
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Milestones
Received: 26 October 2011
Revised: 1 June 2012
Accepted: 6 August 2012
Published: 29 December 2012
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Authors |
| Patrick Gérard | |
| Laboratoire de Mathématiques
d’Orsay CNRS, UMR 8628 Université Paris-Sud XI 91405 Orsay France |
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| Sandrine Grellier | |
| Département de Mathématiques MAPMO-UMR 6628 Université Orléans 45047 Orleans Cedex 2 France |
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