On the Davey-Stewartson systems

Felipe Linares; Gustavo Ponce

Annales de l'I.H.P. Analyse non linéaire (1993)

  • Volume: 10, Issue: 5, page 523-548
  • ISSN: 0294-1449

How to cite

top

Linares, Felipe, and Ponce, Gustavo. "On the Davey-Stewartson systems." Annales de l'I.H.P. Analyse non linéaire 10.5 (1993): 523-548. <http://eudml.org/doc/78315>.

@article{Linares1993,
author = {Linares, Felipe, Ponce, Gustavo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {local well-posedness results; weighted Sobolev spaces},
language = {eng},
number = {5},
pages = {523-548},
publisher = {Gauthier-Villars},
title = {On the Davey-Stewartson systems},
url = {http://eudml.org/doc/78315},
volume = {10},
year = {1993},
}

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
PB - Gauthier-Villars
VL - 10
IS - 5
SP - 523
EP - 548
LA - eng
KW - local well-posedness results; weighted Sobolev spaces
UR - http://eudml.org/doc/78315
ER -

References

top
  1. [1] M.J. Ablowitz and R. Haberman, Nonlinear Evolution Equations in Two and Three Dimensions, Phys. Rev. Lett., Vol. 35, 1975, pp. 1185-1188. MR427866
  2. [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. Zbl0557.35110MR751539
  3. [3] M.J. Ablowitz and A. Segur, Solitons and Inverse Scattering Transform, Philadelphia, PA: SIAM, 1981. Zbl0472.35002MR642018
  4. [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. Zbl0384.76016MR483961
  5. [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. Zbl0725.35096
  6. [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. Zbl0694.35170MR1021011
  7. [7] R.R. Coifman and Y. Meyer, Au delà des opérators pseudodifférentiels, Astérisque57, Société Mathématique de France, 1973. Zbl0483.35082MR518170
  8. [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. Zbl0623.47052MR864370
  9. [9] P. Constantin and J.C. Saut, Local Smoothing Properties of Dispersive Equations, J. Am. Math. Soc., Vol. 1, 1989, pp. 413-439. Zbl0667.35061MR928265
  10. [10] H. Cornille, Solutions of the Generalized Nonlinear Schrödinger Equation in Two Spatial Dimensions, J. Math. Phys., Vol. 20, 1979, pp. 199-209. Zbl0425.35087MR517386
  11. [11] A. Davey and K. Stewartson, On Three-Dimensional Packets of Surface Waves, Proc. R. Soc. A., Vol. 338, 1974, pp. 101-110. Zbl0282.76008MR349126
  12. [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. Zbl0351.76016MR443555
  13. [13] A.S. Fokas and P.M. Santini, Coherent Structures in Multidimensions, Phys. Rev. Letters, Vol. 63, 1989, pp. 1329-1333. MR1014640
  14. [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. Zbl0656.76012MR984911
  15. [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. Zbl0727.35111MR1054584
  16. [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. Zbl0535.35069MR839728
  17. [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. Zbl0657.35033MR880978
  18. [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. Zbl0549.34001MR759907
  19. [19] T. Kato, On Nonlinear Schrödinger Equations, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 46, 1987, pp. 113-129. Zbl0632.35038MR877998
  20. [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. Zbl0671.35066MR951744
  21. [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. Zbl0738.35022MR1101221
  22. [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. Zbl0786.35121MR1230709
  23. [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. Zbl0808.35128MR1211741
  24. [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. Zbl0372.35001MR512086
  25. [25] M. Tsutsumi, Decay of Weaks Solutions for the D-S System, Report of Science & Engineering Research Lab. Waseda University, 1991. 
  26. [26] Y. Tsutsumi, L2-Solutions for the Nonlinear Schrödinger Equations and Nonlinear Groups, Funk. Ekva., Vol. 30, 1987, pp. 115-125. Zbl0638.35021MR915266
  27. [27] P. Sjölin, Regularity of Solutions to the Schrödinger Equations, Duke Math. J., Vol. 55, 1987, pp. 699-715. Zbl0631.42010MR904948
  28. [28] L. Vega, The Schrödinger Equation: Pointwise Convergence to the Initial Data, Proc. Amer. Math. Soc., Vol. 102, 1988, pp. 874-878. Zbl0654.42014MR934859
  29. [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. Zbl0611.35079

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.