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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you