Free access
Issue
ESAIM: M2AN
Volume 40, Number 6, November-December 2006
Page(s) 961 - 990
DOI http://dx.doi.org/10.1051/m2an:2007004
Published online 15 February 2007
  1. H. Added and S. Added, Equation of Langmuir turbulence and nonlinear Schrödinger equation: smoothness and approximation. J. Funct. Anal. 79 (1988) 183–210. [CrossRef] [MathSciNet]
  2. B. Bidégaray, On a nonlocal Zakharov equation. Nonlinear Anal. 25 (1995) 247–278. [CrossRef] [MathSciNet]
  3. M. Colin and T. Colin, On a quasilinear Zakharov System describing laser-plasma interactions. Diff. Int. Eqs. 17 (2004) 297–330.
  4. T. Colin and G. Metivier, Instabilities in Zakharov Equations for Laser Propagation in a Plasma, Phase Space Analysis of PDEs, A. Bove, F. Colombini, and D. Del Santo, Eds., Progress in Nonlinear Differential Equations and Their Applications, Birkhauser (2006).
  5. J.-L. Delcroix and A. Bers, Physique des plasmas 1, 2. Inter Editions-Editions du CNRS (1994).
  6. J. Ginibre, Y. Tsutsumi and G. Velo, On the Cauchy problem for the Zakharov system. J. Funct. Anal. 151 (1997) 384–436. [CrossRef] [MathSciNet]
  7. L. Glangetas and F. Merle, Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. Comm. Math. Phys. 160 (1994) 173–215. [CrossRef] [MathSciNet]
  8. L. Glangetas and F. Merle, Concentration properties of blow up solutions and instability results for Zakharov equation in dimension two. II. Comm. Math. Phys. 160 (1994) 349–389. [CrossRef] [MathSciNet]
  9. R.T. Glassey, Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension. Math. Comp. 58 (1992) 83–102. [CrossRef] [MathSciNet]
  10. C.E. Kenig, G. Ponce and L. Vega, Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Invent. Math. 134 (1998) 489–545. [CrossRef] [MathSciNet]
  11. F. Linares, G. Ponce and J.C. Saut, On a degenerate Zakharov system. Bull. Braz. Math. Soc. New Series 36 (2005) 1–23. [CrossRef]
  12. T. Ozawa and Y. Tsutsumi, Existence and smoothing effect of solution for the Zakharov equations. Publ. Res. Inst. Math. Sci. 28 (1992) 329–361. [CrossRef] [MathSciNet]
  13. G.L. Payne, D.R. Nicholson and R.M. Downie, Numerical Solution of the Zakharov Equations. J. Compt. Phys. 50 (1983) 482–498. [CrossRef]
  14. G. Riazuelo. Étude théorique et numérique de l'influence du lissage optique sur la filamentation des faisceaux lasers dans les plasmas sous-critiques de fusion inertielle. Ph.D. thesis, University of Paris XI.
  15. D.A. Russel, D.F. Dubois and H.A. Rose. Nonlinear saturation of simulated Raman scattering in laser hot spots. Phys. Plasmas 6 (1999) 1294–1317. [CrossRef]
  16. K.Y. Sanbomatsu, Competition between Langmuir wave-wave and wave-particule interactions. Ph.D. thesis, University of Colorado, Department of Astrophysical (1997).
  17. S. Schochet and M. Weinstein, The nonlinear Schrödinger limit of the Zakharov equations governing Langmuir turbulence. Comm. Math. Phys. 106 (1986) 569–580. [CrossRef] [MathSciNet]
  18. C. Sulem and P.-L. Sulem, Quelques résultats de régularité pour les équations de la turbulence de Langmuir. C. R. Acad. Sci. Paris Sér. A-B 289 (1979) 173–176.
  19. C. Sulem and P.-L. Sulem, The nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse. Appl. Math. Sci. 139, Springer (1999).
  20. B. Texier, Derivation of the Zakharov equations. Arch. Rat. Mech. Anal. (to appear).
  21. V.E. Zakharov, S.L. Musher and A.M. Rubenchik, Hamiltonian approach to the description of nonlinear plasma phenomena. Phys. Reports 129 (1985) 285–366. [CrossRef]

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