Space-modulated stability and averaged dynamics
Journées équations aux dérivées partielles (2015), article no. 8, 15 p.

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.

DOI: 10.5802/jedp.637
Classification: 35B10,  35B35,  35K59,  35P05,  35Q53,  37K45
Keywords: periodic traveling waves, stability, modulation
Rodrigues, Luis Miguel 1

1 Université de Rennes 1 IRMAR, UMR CNRS 6625 263 avenue du General Leclerc F-35042 Rennes Cedex France
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Rodrigues, Luis Miguel. Space-modulated stability and averaged dynamics. Journées équations aux dérivées partielles (2015), article  no. 8, 15 p. doi : 10.5802/jedp.637. http://www.numdam.org/articles/10.5802/jedp.637/

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