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Effective integrable dynamics for some nonlinear wave equation

Abstract : We consider the following degenerate half wave equation on the one dimensional torus $$\quad i\partial _t u-|D|u=|u|^2u, \; u(0,\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system-- the cubic Szegö equation. As a consequence, we prove an instability result for large $H^s$ norms of solutions of this wave equation.
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Submitted on : Tuesday, October 25, 2011 - 5:06:29 PM
Last modification on : Monday, December 23, 2019 - 3:50:10 PM
Document(s) archivé(s) le : Thursday, January 26, 2012 - 2:45:10 PM

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  • HAL Id : hal-00635686, version 1
  • ARXIV : 1110.5719

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Patrick Gerard, Sandrine Grellier. Effective integrable dynamics for some nonlinear wave equation. Analysis and PDEs, 2012, 5-5, pp.1139-1155. ⟨hal-00635686⟩

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