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.
@article{JEDP_2015____A8_0,
author = {Rodrigues, Luis Miguel},
title = {Space-modulated stability and averaged dynamics},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {2015},
pages = {1-15},
doi = {10.5802/jedp.637},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_2015____A8_0}
}
Rodrigues, Luis Miguel. Space-modulated stability and averaged dynamics. Journées équations aux dérivées partielles, (2015), pp. 1-15. doi : 10.5802/jedp.637. http://gdmltest.u-ga.fr/item/JEDP_2015____A8_0/
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