About nonlinear geometric optics Eric Dumas Prepublication de l'Institut Fourier no 685 (2005) www-fourier.ujf-grenoble.fr/prepublications.html Abstract We give an idea of the evolution of mathematical nonlinear geometric optics from its foundation by Lax in 1957, and present applications in various fields of mathematics and physics. Keywords: high-frequency analysis, nonlinear geometric optics, resonances, caus- tics, reflections, shocks, boundary layers, diffractive optics, large amplitudes, trans- parency, long waves. Resume Nous presentons differents resultats d'optique geometrique non-lineaire, en re- montant aux premiers resultats de Lax en 1957 (dans le cadre lineaire), jusqu'aux progres recents et a leurs applications en mathematique et en physique. Mots-cles : analyse haute-frequence, optique geometrique non-lineaire, resonances, caustiques, reflexions, chocs, couches limites, optique diffractive, grandes solutions, transparence, ondes longues. 2000 Mathematics Subject Classification : 35-02, 35B25, 35C20, 35Qxx.
- profile equations
- large amplitude
- initial phase
- geometric optics
- nonlinear geometric
- differents resultats d'optique
- equations takes
- optique diffractive