no. 1
Coherent and focusing multidimensional nonlinear geometric optics
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 28 (1995) no. 1, pp. 51-113. 
@article{ASENS_1995_4_28_1_51_0,
     author = {Joly, J.-L. and M\'etivier, G. and Rauch, J.},
     title = {Coherent and focusing multidimensional nonlinear geometric optics},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {51--113},
     publisher = {Elsevier},
     volume = {Ser. 4, 28},
     number = {1},
     year = {1995},
     doi = {10.24033/asens.1709},
     mrnumber = {95k:35035},
     zbl = {0836.35087},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1709/}
}
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Joly, J.-L.; Métivier, G.; Rauch, J. Coherent and focusing multidimensional nonlinear geometric optics. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 28 (1995) no. 1, pp. 51-113. doi : 10.24033/asens.1709. http://archive.numdam.org/articles/10.24033/asens.1709/

[C] C. Cheverry, Oscillations de faible amplitude pour les systèmes 2 × 2 de lois de conservations, preprint Rennes, 1993. | Zbl

[D] J.-M. Delort, Oscillations semi-linéaires multiphasées compatibles en dimension 2 et 3 d'espace (Comm. in Partial Diff. Equ., Vol. 16, 1991, pp. 845-872). | MR | Zbl

[DPM] R. Diperna and A. Majda, The validity of geometric optics for weak solutions (Comm. in Math. Phys., Vol. 98, 1985, pp. 313-347). | MR | Zbl

[G1] O. Gues, Développements asymptotiques de solutions exactes de systèmes hyperboliques quasi-linéaires (Asymptotic Analysis, Vol. 6, 1993, pp. 675-678). | MR | Zbl

[G2] O. Gues, Ondes multidimensionnelles ε-statifiées et oscillations (Duke Math. J., Vol. 68, 1992, pp. 401-446). | MR | Zbl

[HMR] J. Hunter, A. Majda and R. Rosales, Resonantly Interacting Weakly Nonlinear Hyperbolic Waves II : Several Space Variables (Stud. Appl. Math., Vol. 75, 1986, pp. 187-226). | MR | Zbl

[JMR1] J.-L. Joly, G. Metivier and J. Rauch, Resonant One Dimensional Nonlinear Geometric Optics (to appear in J. Funct. Analysis, Vol. 114, No. 1, 1993, pp. 106-231). | MR | Zbl

[JMR2] J.-L. Joly, G. Metivier and J. Rauch, Formal and Rigorous Nonlinear High Frequency Hyperbolic Waves, in Proceedings of Varenna Conference on Nonlinear Hyperbolic Equations and Field Theory, June 1990, M. K. MURPTY, S. SPAGNOLO eds. (Pitman Research Note in Math. Series, 1992, 121, p. 143). | Zbl

[JMR3] J.-L. Joly, G. Metivier and J. Rauch, Remarques sur l'optique géométrique non linéaire multidimensionnelle, in Séminaire Équations aux dérivées partielles de l'École Polytechnique 1990-1991, Exposé n° 1. | Numdam | Zbl

[JMR4] J.-L. Joly, G. Metivier and J. Rauch, Coherent Nonlinear Waves and the Wiener Algebra (Ann. Inst. Fourier, t. 44, 1994, pp. 167-196). | Numdam | MR | Zbl

[JMR5] J.-L. Joly, G. Metivier and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillary waves (to appear in Duke Math. J., Vol. 70, No. 2, 1993, pp. 373-404). | MR | Zbl

[JMR6] J.-L. Joly, G. Metivier and J. Rauch, Dense oscillations for the compressible 2-D Euler equations, in Non Linear Partial Differential Equations, Séminaire Collège de France 1992-1993, Pitmann Publ.

[JR1] J.-L. Joly and J. Rauch, Justification of Multidimensional Single Phase Semilinear Geometric Optics (Trans. Amer. Math. Soc., Vol. 330, 1992, pp. 599-625). | MR | Zbl

[JR2] J.-L. Joly and J. Rauch, Nonlinear Resonance can Create Dense Oscillations, in Microlocal Analysis and Nonlinear Waves, M. BEALS, R. MELROSE and J. B. RAUCH eds. (IMA Volumes in Math. and its Application, Vol. 30, Springer-Verlag). | MR | Zbl

[Ka1] L. A. Kalyakin, Long Waves Asymptotics of Solutions of Nonlinear Systems of Equations with Dispersion (Dokl. An SSSR, Vol. 288, n° 4, 1986, and Soviet Math. Dokl., Vol. 33, n° 3, 1986, pp. 769-774). | MR | Zbl

[Ka2] L. A. Kalyakin, Asymptotic Decay of a One Dimensional Wave Packet in a Nonlinear Dispersive Medium (Math. Sbornik Translation, Vol. 60, n° 2, 1988, pp. 457-484). | MR | Zbl

[Ka3] L. A. Kalyakin, Long Waves Asymptotics. Integrable Equations as Asymptotic Limit of Nonlinear Systems (Russian Mth. Surveys, Vol. 44, n° 1, 1989, pp. 3-42). | MR | Zbl

[Ke] J. Keller, On solutions of nonlinear waves operators (Comm. Pure App. Math., Vol. 10, 1957, pp. 523-530). | MR | Zbl

[L1] P. Lax, Shock Waves and Entropy, in Contribution to Nonlinear Analysis, ZARANTONELLO ed., Academic Press, NY, 1971, pp. 603-634. | MR | Zbl

[L2] P. Lax, Asymptotic solutions of oscillatory initial value problems (Duke Math. J., Vol. 24, 1957, pp. 627-645). | MR | Zbl

[MR] A. Majda and R. Rosales, Resonantly Interacting Weakly Nonlinear Hyperbolic Waves I : a Single Space Variables Stud. Appl. Math., Vol. 71, 1984, pp. 149-179). | MR | Zbl

[RR] J. Rauch and M. Reed, Striated solutions of semilinear twospeed wave equations (Indiana Univ. Math. J., Vol. 34, 1985, pp. 337-353). | MR | Zbl

[S1] S. Schochet, Fast singular limits of hyperbolic partial differential equations (to appear in J. Diff. Equ.). | Zbl

[S2] S. Schochet, Resonant nonlinear geometric optics for weak solutions of conservations laws, preprint 1992.

[ST] M. Sablé Tougeron, Justification de l'optique géométrique faiblement non linéaire pour le problème mixte : cas des concentrations, preprint, 1993.

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