@article{SEDP_1995-1996____A17_0, author = {Donnat, P. and Joly, J.-L. and M\'etivier, G. and Rauch, J.}, title = {Diffractive nonlinear geometric optics}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:17}, pages = {1--23}, publisher = {Ecole Polytechnique, Centre de Math\'ematiques}, year = {1995-1996}, mrnumber = {1604366}, zbl = {0910.35076}, language = {en}, url = {http://www.numdam.org/item/SEDP_1995-1996____A17_0/} }
TY - JOUR AU - Donnat, P. AU - Joly, J.-L. AU - Métivier, G. AU - Rauch, J. TI - Diffractive nonlinear geometric optics JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:17 PY - 1995-1996 SP - 1 EP - 23 PB - Ecole Polytechnique, Centre de Mathématiques UR - http://www.numdam.org/item/SEDP_1995-1996____A17_0/ LA - en ID - SEDP_1995-1996____A17_0 ER -
%0 Journal Article %A Donnat, P. %A Joly, J.-L. %A Métivier, G. %A Rauch, J. %T Diffractive nonlinear geometric optics %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:17 %D 1995-1996 %P 1-23 %I Ecole Polytechnique, Centre de Mathématiques %U http://www.numdam.org/item/SEDP_1995-1996____A17_0/ %G en %F SEDP_1995-1996____A17_0
Donnat, P.; Joly, J.-L.; Métivier, G.; Rauch, J. Diffractive nonlinear geometric optics. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1995-1996), Exposé no. 17, 23 p. http://www.numdam.org/item/SEDP_1995-1996____A17_0/
[D] Quelques contributions mathématiques en optique non linéaire, thèse, École Polytechnique, 1994.
,[DR 1] Dispersive nonlinear geometric optics, preprint | MR | Zbl
and ,[DR 2] Diffractive nonlinear geometric optics for dispersive hyperbolic systems, in preparation.
and ,[Go] Global oscillatory waves for second order quasilinear wave equations, Trans. Amer. Math. Soc., 346(2)(1994), 523-547. | MR | Zbl
,[G 1] Développements asymptotiques de solutions exactes de systèmes hyperboliques quasilinéaires, Asymptotic Anal., 6(1993), 241-269. | MR | Zbl
,[G 2] Ondes multidimensionnelles ε-stratifiées et oscillations, Duke Math. J., 68(1992), 401-446. | Zbl
,[HMR] Resonantly interacting weakly nonlinear hyperbolic waves II: several space variables, Stud. Appl. Math., 75(1986), 187-226. | MR | Zbl
, , and ,[JMR 1] Resonant one dimensional nonlinear geometric optics J. Funct. Anal., 114(1993),106-231. | MR | Zbl
, , and ,[JMR 2] Coherent and focusing multidimensional nonlinear geometric optics, Annales de L'École Normale Supérieure de Paris, 28(1995), 51-113. | Numdam | MR | Zbl
, , and ,[JMR 3] Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J., 70(1993), 373-404. | MR | Zbl
, , and ,[JMR 4] Coherent nonlinear waves and the Wiener algebra, Ann. Inst. Fourier, 44(1994), 167-196. | Numdam | MR | Zbl
, , and ,[JMR 5] Nonlinear oscillations beyond caustics, Comm. Pure and Appl. Math., (1996). | MR | Zbl
, , and ,[JMR 6] Rectification in diffractive nonlinear geometric optics. in preparation.
, , and ,[JMR 7] Multiphase diffractive nonlinear geometric optics, in preparation.
, , and ,[JR] Justification of multidimensional single phase semilinear geometric optics, Trans. Amer. Math. Soc., 330(1992), 599-625. | MR | Zbl
and ,[Lax] Oscillatory solutions of oscillatory initial value problems, Duke Math. J., 24(1957), 627-645. | MR | Zbl
,[MRS] A canonical system of integrodifferential equations arising in resonant nonlinear acoustics, Stud. Appl. Math., 79(1988), 205-262. | MR | Zbl
, and ,[R] Lectures on geometric optics, IAS-Park City Summer School on Nonlinear Waves, July, 1995.
,[Se ] Oscillations non linéaires des systèmes hyperboliques: méthodes et résultats qualitatifs, Ann. Inst. Henri Poincaré, 8(1991) 351-417. | Numdam | MR | Zbl
,[Sch ] Fast singular limits of hyperbolic partial differential equations, J. Diff. Eq., 114(1994), 474-512. | MR | Zbl
,[T] Solutions oscillantes des équations de Carleman, Séminaire Goulaouic-Schwartz, École Polytechnique, Paris, année 1980-1981. | Numdam | MR | Zbl
,[Wa] Analytic solutions and resonant solutions of hyperbolic partial differential equations, PhD Thesis, University of Michigan, 1993.
,[Wi ] Resonant reflection of multidimensional semilinear oscillations, Comm. Partial Diff. Eq., 18(1993), 1901-1959. | MR | Zbl
,