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2012 Effective integrable dynamics for a certain nonlinear wave equation
Patrick Gérard, Sandrine Grellier
Anal. PDE 5(5): 1139-1155 (2012). DOI: 10.2140/apde.2012.5.1139

Abstract

We consider the following degenerate half-wave equation on the one-dimensional torus:

i t u | D | u = | u | 2 u , u ( 0 , ) = u 0 .

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 Hs norms of solutions of this wave equation.

Citation

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Patrick Gérard. Sandrine Grellier. "Effective integrable dynamics for a certain nonlinear wave equation." Anal. PDE 5 (5) 1139 - 1155, 2012. https://doi.org/10.2140/apde.2012.5.1139

Information

Received: 26 October 2011; Revised: 1 June 2012; Accepted: 6 August 2012; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1268.35013
MathSciNet: MR3022852
Digital Object Identifier: 10.2140/apde.2012.5.1139

Subjects:
Primary: 35B34, 35B40, 37K55

Rights: Copyright © 2012 Mathematical Sciences Publishers

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