Free Access
Volume 35, Number 1, January/February 2001
Page(s) 35 - 55
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.
  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.
  3. C. Besse, Analyse numérique des systèmes de Davey-Stewartson. Ph.D. thesis, University of Bordeaux I, France (1998).
  4. C. Besse, B. Bidégaray and S. Descombes, Accuracy of the split-step schemes for the Nonlinear Schrödinger Equation. (In preparation).
  5. B. Bidégaray, On the Cauchy problem for systems occurring in nonlinear optics. Adv. Differential Equations 3 (1998) 473-496. [MathSciNet]
  6. B. Bidégaray, The Cauchy problem for Schrödinger-Debye equations. Math. Models Methods Appl. Sci. 10 (2000) 307-315. [CrossRef] [MathSciNet]
  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.
  8. T. Cazenave, An introduction to nonlinear Schrödinger equations. Textos de métodos matemáticos 26, Rio de Janeiro (1990).
  9. T. Cazenave, Blow-up and Scattering in the nonlinear Schrödinger equation. Textos de métodos matemáticos 30, Rio de Janeiro (1994).
  10. T. Colin and P. Fabrie, Semidiscretization in time for nonlinear Schrödinger-waves equations. Discrete Contin. Dynam. Systems 4 (1998) 671-690. [CrossRef] [MathSciNet]
  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]
  12. B.O. Dia and M. Schatzman, Estimations sur la formule de Strang. C. R. Acad. Sci. Paris, Sér. I 320 (1995) 775-779.
  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).
  14. P. Donnat, Quelques contributions mathématiques en optique non linéaire. Ph.D. thesis, École Polytechnique, France (1994).
  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]
  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]
  17. A.C. Newell and J.V. Moloney, Nonlinear Optics. Addison-Wesley (1992).
  18. J.M. Sanz-Serna Methods for the Numerical Solution of the Nonlinear Schrödinger Equation. Math. Comput. 43 (1984) 21-27
  19. Y. R. Shen, The Principles of Nonlinear Optics. Wiley, New York (1984).
  20. G. Strang On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (1968) 506-517.
  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]
  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]

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