Diffractive nonlinear geometric optics

P. Donnat; J.-L. Joly; G. Métivier; J. Rauch

Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996)

  • page 1-23

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Donnat, P., et al. "Diffractive nonlinear geometric optics." Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996): 1-23. <http://eudml.org/doc/112128>.

@article{Donnat1995-1996,
author = {Donnat, P., Joly, J.-L., Métivier, G., Rauch, J.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {geometric optic approach; Schrödinger equation; fast oscillating plane wave; slow modulating small amplitude; transport equation},
language = {eng},
pages = {1-23},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Diffractive nonlinear geometric optics},
url = {http://eudml.org/doc/112128},
year = {1995-1996},
}

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)
PY - 1995-1996
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 23
LA - eng
KW - geometric optic approach; Schrödinger equation; fast oscillating plane wave; slow modulating small amplitude; transport equation
UR - http://eudml.org/doc/112128
ER -

References

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  3. [DR 2] P. Donnat and J. Rauch, Diffractive nonlinear geometric optics for dispersive hyperbolic systems, in preparation. Zbl0881.35078
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  8. [JMR 1] J.-L. Joly, G. Metivier, and J. Rauch, Resonant one dimensional nonlinear geometric opticsJ. Funct. Anal., 114(1993),106-231. Zbl0851.35023MR1220985
  9. [JMR 2] J.-L. Joly, G. Metivier, and J. Rauch, Coherent and focusing multidimensional nonlinear geometric optics, Annales de L'École Normale Supérieure de Paris, 28(1995), 51-113. Zbl0836.35087MR1305424
  10. [JMR 3] J.-L. Joly, G. Metivier, and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves, Duke Math. J., 70(1993), 373-404. Zbl0815.35066MR1219817
  11. [JMR 4] J.-L. Joly, G. Metivier, and J. Rauch, Coherent nonlinear waves and the Wiener algebra, Ann. Inst. Fourier, 44(1994), 167-196. Zbl0791.35019MR1262884
  12. [JMR 5] J.-L. Joly, G. Metivier, and J. Rauch, Nonlinear oscillations beyond caustics, Comm. Pure and Appl. Math., (1996). Zbl0862.35066MR1377560
  13. [JMR 6] J.-L. Joly, G. Metivier, and J. Rauch, Rectification in diffractive nonlinear geometric optics. in preparation. Zbl0928.35093
  14. [JMR 7] J.-L. Joly, G. Metivier, and J. Rauch, Multiphase diffractive nonlinear geometric optics, in preparation. Zbl0910.35076
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  17. [MRS] A. Majda, R. Rosales and M. Schonbeck, A canonical system of integrodifferential equations arising in resonant nonlinear acoustics, Stud. Appl. Math., 79(1988), 205-262. Zbl0669.76103MR975485
  18. [R] J. Rauch, Lectures on geometric optics, IAS-Park City Summer School on Nonlinear Waves, July, 1995. 
  19. [Se ] D. Serre, Oscillations non linéaires des systèmes hyperboliques: méthodes et résultats qualitatifs, Ann. Inst. Henri Poincaré, 8(1991) 351-417. Zbl0810.35060MR1127931
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  22. [Wa] T. Wagenmaker, Analytic solutions and resonant solutions of hyperbolic partial differential equations, PhD Thesis, University of Michigan, 1993. 
  23. [Wi ] M. Williams, Resonant reflection of multidimensional semilinear oscillations, Comm. Partial Diff. Eq., 18(1993), 1901-1959. Zbl0788.35078MR1243530

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