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Journées équations aux dérivées partielles

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Luis Miguel Rodrigues
Space-modulated stability and averaged dynamics
Journées équations aux dérivées partielles (2015), Exp. No. 8, 15 p., doi: 10.5802/jedp.637
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Class. Math.: 35B10, 35B35, 35K59, 35P05, 35Q53, 37K45
Mots clés: periodic traveling waves, stability, modulation

Résumé - Abstract

In this brief note we give a brief overview of the comprehensive theory, recently obtained by the author jointly with Johnson, Noble and Zumbrun, that describes the nonlinear dynamics about spectrally stable periodic waves of parabolic systems and announce parallel results for the linearized dynamics near cnoidal waves of the Korteweg–de Vries equation. The latter are expected to contribute to the development of a dispersive theory, still to come.

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