On the Davey-Stewartson systems
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 5, pp. 523-548.
@article{AIHPC_1993__10_5_523_0,
     author = {Linares, Felipe and Ponce, Gustavo},
     title = {On the {Davey-Stewartson} systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {523--548},
     publisher = {Gauthier-Villars},
     volume = {10},
     number = {5},
     year = {1993},
     mrnumber = {1249105},
     zbl = {0807.35136},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1993__10_5_523_0/}
}
TY  - JOUR
AU  - Linares, Felipe
AU  - Ponce, Gustavo
TI  - On the Davey-Stewartson systems
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1993
SP  - 523
EP  - 548
VL  - 10
IS  - 5
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1993__10_5_523_0/
LA  - en
ID  - AIHPC_1993__10_5_523_0
ER  - 
%0 Journal Article
%A Linares, Felipe
%A Ponce, Gustavo
%T On the Davey-Stewartson systems
%J Annales de l'I.H.P. Analyse non linéaire
%D 1993
%P 523-548
%V 10
%N 5
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1993__10_5_523_0/
%G en
%F AIHPC_1993__10_5_523_0
Linares, Felipe; Ponce, Gustavo. On the Davey-Stewartson systems. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 5, pp. 523-548. http://archive.numdam.org/item/AIHPC_1993__10_5_523_0/

[1] M.J. Ablowitz and R. Haberman, Nonlinear Evolution Equations in Two and Three Dimensions, Phys. Rev. Lett., Vol. 35, 1975, pp. 1185-1188. | MR

[2] M.J. Ablowitz and A.S. Fokas, On the Inverse Scattering Transform of Multidimensional Nonlinear Equations, J. Math. Phys., Vol. 25, 1984, pp. 2494-2505. | MR | Zbl

[3] M.J. Ablowitz and A. Segur, Solitons and Inverse Scattering Transform, Philadelphia, PA: SIAM, 1981. | MR | Zbl

[4] D. Anker and N.C. Freeman, On the Solition Solutions of the Davey-Stewartson Equation for Long Waves, Proc. R. Soc. A, Vol. 360, 1978, pp. 529-540. | MR | Zbl

[5] R. Beals and R.R. Coifman, The Spectral Problem for the Davey-Stewartson and Ishimori Hierarchies, Proc. Conf. on Nonlinear Evolution Equations: Integrability and Spectral Methods, Manchester, U.K. 1988.

[6] T. Cazenave and F.B. Weissler, Some Remarks on the Nonlinear Schrödinger Equation in the Critical Case, Lect. Notes in Math., Vol. 1394, 1989, pp. 18-29. | MR | Zbl

[7] R.R. Coifman and Y. Meyer, Au delà des opérators pseudodifférentiels, Astérisque 57, Société Mathématique de France, 1973. | Numdam | MR | Zbl

[8] R.R. Coifman and Y. Meyer, Nonlinear Harmonic Analysis, Operator Theory and P.D.E., Beijing Lectures in Harmonic Analysis, Princeton University Press, 1986, pp. 3-45. | MR | Zbl

[9] P. Constantin and J.C. Saut, Local Smoothing Properties of Dispersive Equations, J. Am. Math. Soc., Vol. 1, 1989, pp. 413-439. | MR | Zbl

[10] H. Cornille, Solutions of the Generalized Nonlinear Schrödinger Equation in Two Spatial Dimensions, J. Math. Phys., Vol. 20, 1979, pp. 199-209. | MR | Zbl

[11] A. Davey and K. Stewartson, On Three-Dimensional Packets of Surface Waves, Proc. R. Soc. A., Vol. 338, 1974, pp. 101-110. | MR | Zbl

[12] V.D. Djordjevic and L.P. Redekopp, On Two-Dimensional Packets of Capillarity-Gravity Waves, J. Fluid Mech., Vol. 79, 1977, pp. 703-714. | MR | Zbl

[13] A.S. Fokas and P.M. Santini, Coherent Structures in Multidimensions, Phys. Rev. Letters, Vol. 63, 1989, pp. 1329-1333. | MR

[14] J.M. Ghidaglia and J.C. Saut, Sur le problème de Cauchy pour les équations de Davey-Stewartson, C. R. Acad. Sci. Paris, T. 308, Series I, 1989, pp. 115-120. | MR | Zbl

[15] J.M. Ghidaglia and J.C. Saut, On the Initial Value Problem for the Davey-Stewartson System, Nonlinearity, Vol. 3, 1990, pp. 475-506. | MR | Zbl

[16] J. Ginibre and G. Velo, Scattering Theory in the Energy Space for a Class of Nonlinear Schrödinger Equations, J. Math. Pure Appl., Vol. 64, 1985, pp. 363-401. | MR | Zbl

[17] N. Hayashi, K. Nakamitsi and M. Tsutsumi, On Solutions to the Initial Value Problem for the Nonlinear Schrödinger Equations, J. Funt. Anal., Vol. 71, 1987, pp. 218-245. | MR | Zbl

[18] T. Kato, On the Cauchy Problem for the (Generalized) Korteweg-de Vries Equation, Advances in Mathematics Supplementary Studies, Studies in Appl. Math., Vol. 8, 1983, pp. 891-907. | MR | Zbl

[19] T. Kato, On Nonlinear Schrödinger Equations, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 46, 1987, pp. 113-129. | Numdam | MR | Zbl

[20] T. Kato and G. Ponce, Commutator Estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 891-907. | MR | Zbl

[21] C.E. Kenig, G. Ponce and L. Vega, Oscillatory Integrals and Regularity of Dispersive Equations, Indiana University Math. J., Vol. 40, 1991, pp. 33-69. | MR | Zbl

[22] C.E. Kenig, G. Ponce and L. Vega, Small Solutions to Nonlinear Schrödinger Equations, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 10, 1993, pp. 255- 288. | Numdam | MR | Zbl

[23] C.E. Kenig, G. Ponce and L. Vega, Well-Posedness and Scattering Results for the Generalized Korteweg-de Vries equation via Contraction Principle, Comm. Pure Appl. Math., Vol. 46, 1993, pp. 527-620. | MR | Zbl

[24] R. Strichartz, Restrictions of Fourier Transforms to Quadratic Surfaces and Decay of Solutions of Wave Equations, Duke Math. J., Vol. 44, 1977, pp. 705-714. | MR | Zbl

[25] M. Tsutsumi, Decay of Weaks Solutions for the D-S System, Report of Science & Engineering Research Lab. Waseda University, 1991.

[26] Y. Tsutsumi, L2-Solutions for the Nonlinear Schrödinger Equations and Nonlinear Groups, Funk. Ekva., Vol. 30, 1987, pp. 115-125. | MR | Zbl

[27] P. Sjölin, Regularity of Solutions to the Schrödinger Equations, Duke Math. J., Vol. 55, 1987, pp. 699-715. | MR | Zbl

[28] L. Vega, The Schrödinger Equation: Pointwise Convergence to the Initial Data, Proc. Amer. Math. Soc., Vol. 102, 1988, pp. 874-878. | MR | Zbl

[29] V.E. Zakharov and E.A. Kuznetson, Multi-Scale Expansions in the Theory of Systems Integrable by the Inverse Scattering Method, Physica D, Vol. 18, 1986, pp. 455-463. | Zbl