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.
Mots clés : periodic traveling waves, stability, modulation
@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}, eid = {8}, pages = {1--15}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2015}, doi = {10.5802/jedp.637}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.637/} }
TY - JOUR AU - Rodrigues, Luis Miguel TI - Space-modulated stability and averaged dynamics JO - Journées équations aux dérivées partielles PY - 2015 SP - 1 EP - 15 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.637/ DO - 10.5802/jedp.637 LA - en ID - JEDP_2015____A8_0 ER -
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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