Free Access
Issue
ESAIM: M2AN
Volume 35, Number 1, January/February 2001
Page(s) 35 - 55
DOI https://doi.org/10.1051/m2an:2001106
Published online 15 April 2002
  1. G.D. Akrivis, V.A. Dougalis, O.A. Karakashian and W.R. McKinney, Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrödinger equation (1997). Preprint. [Google Scholar]
  2. C. Besse, Schéma de relaxation pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson. C. R. Acad. Sci., Sér. I 326 (1998) 1427-1432. [Google Scholar]
  3. C. Besse, Analyse numérique des systèmes de Davey-Stewartson. Ph.D. thesis, University of Bordeaux I, France (1998). [Google Scholar]
  4. C. Besse, B. Bidégaray and S. Descombes, Accuracy of the split-step schemes for the Nonlinear Schrödinger Equation. (In preparation). [Google Scholar]
  5. B. Bidégaray, On the Cauchy problem for systems occurring in nonlinear optics. Adv. Differential Equations 3 (1998) 473-496. [MathSciNet] [Google Scholar]
  6. B. Bidégaray, The Cauchy problem for Schrödinger-Debye equations. Math. Models Methods Appl. Sci. 10 (2000) 307-315. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.L. Bona, V.A. Dougalis, O.A. Karakashian and W.R. McKinney, Conservative, high-order numerical schemes for the generalized Korteweg-de Vries equation. Philos. Trans. Roy. Soc. London, Ser. A 351 (1995) 107-164. [Google Scholar]
  8. T. Cazenave, An introduction to nonlinear Schrödinger equations. Textos de métodos matemáticos 26, Rio de Janeiro (1990). [Google Scholar]
  9. T. Cazenave, Blow-up and Scattering in the nonlinear Schrödinger equation. Textos de métodos matemáticos 30, Rio de Janeiro (1994). [Google Scholar]
  10. T. Colin and P. Fabrie, Semidiscretization in time for nonlinear Schrödinger-waves equations. Discrete Contin. Dynam. Systems 4 (1998) 671-690. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Delfour, M. Fortin and G. Payre, Finite-difference solutions of a nonlinear Schrödinger equation. J. Comput. Phys. 44 (1981) 277-288. [CrossRef] [MathSciNet] [Google Scholar]
  12. B.O. Dia and M. Schatzman, Estimations sur la formule de Strang. C. R. Acad. Sci. Paris, Sér. I 320 (1995) 775-779. [Google Scholar]
  13. L. Di Menza, Approximations numériques d'équations de Schrödinger non linéaires et de modèles associés. Ph.D. thesis, University of Bordeaux I, France (1995). [Google Scholar]
  14. P. Donnat, Quelques contributions mathématiques en optique non linéaire. Ph.D. thesis, École Polytechnique, France (1994). [Google Scholar]
  15. G. Fibich and G.C. Papanicolaou, Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension. SIAM J. Appl. Math. 60 (2000) 183-240. [CrossRef] [MathSciNet] [Google Scholar]
  16. R.T. Glassey, Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension. Math. Comput. 58 (1992) 83-102. [CrossRef] [MathSciNet] [Google Scholar]
  17. A.C. Newell and J.V. Moloney, Nonlinear Optics. Addison-Wesley (1992). [Google Scholar]
  18. J.M. Sanz-Serna Methods for the Numerical Solution of the Nonlinear Schrödinger Equation. Math. Comput. 43 (1984) 21-27 [Google Scholar]
  19. Y. R. Shen, The Principles of Nonlinear Optics. Wiley, New York (1984). [Google Scholar]
  20. G. Strang On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 506-517. [Google Scholar]
  21. C. Sulem, P.L. Sulem and A. Patera, Numerical Simulation of Singular Solutions to the Two-Dimensional Cubic Schrödinger Equation. Commun. Pure Appl. Math. 37 (1984) 755-778. [CrossRef] [Google Scholar]
  22. J.A.C. Weideman and B.M. Herbst, Split-step methods for the solution of the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 23 (1986) 485-507. [CrossRef] [MathSciNet] [Google Scholar]

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