Free Access
Issue
ESAIM: PS
Volume 9, June 2005
Page(s) 74 - 97
DOI https://doi.org/10.1051/ps:2005005
Published online 15 November 2005
  1. R. Azencott, Grandes déviations et applications, in École d'été de Probabilité de Saint-Flour, P.L. Hennequin Ed. Springer-Verlag, Berlin. Lect. Notes Math. 774 (1980) 1–176. [CrossRef] [Google Scholar]
  2. A. Badrikian and S. Chevet, Mesures cylindriques, espaces de Wiener et fonctions aléatoires Gaussiennes. Springer-Verlag, Berlin. Lect. Notes Math. 379 (1974). [Google Scholar]
  3. Y.M. Berezansky, Z.G. Sheftel and G.F. Us, Functional Analysis, Vol. 1. Oper. Theor. Adv. Appl. 85 (1997) 125–134. [Google Scholar]
  4. G. Buttazzo, M. Giaquinta and S. Hildebrandt, One-dimensional Variational Problems. Oxford University Press, Oxford. Oxford Lect. Ser. Math. Appl. 15 (1998). [Google Scholar]
  5. T. Cazenave, An Introduction to Nonlinear Schrödinger Equations. Instituto de Matématica-UFRJ Rio de Janeiro, Brazil. Textos de Métodos Matématicos 26 (1993). [Google Scholar]
  6. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge University Press: Cambridge, England. Encyclopedia Math. Appl. (1992). [Google Scholar]
  7. A. de Bouard and A. Debussche, The Stochastic Nonlinear Schrödinger Equation in H1. Stochastic Anal. Appl. 21 (2003) 97–126. [CrossRef] [MathSciNet] [Google Scholar]
  8. A. de Bouard and A. Debussche, On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Probab. Theory Relat. Fields 123 (2002) 76–96. [CrossRef] [Google Scholar]
  9. A. de Bouard and A. Debussche, Finite time blow-up in the additive supercritical nonlinear Schrödinger equation: the real noise case. Contemp. Math. 301 (2002) 183–194. [Google Scholar]
  10. A. Debussche and L. Di Menza, Numerical simulation of focusing stochastic nonlinear Schrödinger equations. Phys. D 162 (2002) 131–154. [CrossRef] [MathSciNet] [Google Scholar]
  11. S.A. Derevyanko, S.K. Turitsyn and D.A. Yakusev, Non-gaussian statistics of an optical soliton in the presence of amplified spontaneaous emission. Optics Lett. 28 (2003) 2097–2099. [CrossRef] [PubMed] [Google Scholar]
  12. J.D. Deuschel and D.W. Stroock, Large Deviations. Academic Press, New York. Pure Appl. Math. (1986). [Google Scholar]
  13. A. Dembo and O. Zeitouni, Large deviation techniques and applications (2nd edition). Springer-Verlag, New York. Appl. Math. 38 (1998). [Google Scholar]
  14. P.D. Drummond and J.F. Corney, Quantum noise in optical fibers. II. Raman jitter in soliton communications. J. Opt. Soc. Am. B 18 (2001) 153–161. [CrossRef] [Google Scholar]
  15. L.C. Evans, Partial Differential Equations. American Mathematical Society, Providence, Rhode Island, Grad. Stud. in Math. 119 (1998). [Google Scholar]
  16. G.E. Falkovich, I. Kolokolov, V. Lebedev and S.K. Turitsyn, Statistics of soliton-bearing systems with additive noise. Phys. Rev. E 63 (2001) 025601(R). [Google Scholar]
  17. G. Falkovich, I. Kolokolov, V. Lebedev, V. Mezentsev and S.K. Turitsyn, Non-Gaussian error probability in optical soliton transmission. Physica D 195 (2004) 1–28. [CrossRef] [MathSciNet] [Google Scholar]
  18. É. Gautier, Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise. Preprint IRMAR, Rennes (2004). Submitted for publication. [Google Scholar]
  19. T. Kato, On Nonlinear Schrödinger Equation. Ann. Inst. H. Poincaré, Phys. Théor. 46 (1987) 113–129. [Google Scholar]
  20. V. Konotop and L. Vázquez, Nonlinear random waves. World Scientific Publishing Co., Inc.: River Edge, New Jersey (1994). [Google Scholar]
  21. R.O. Moore, G. Biondini and W.L. Kath, Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems. Optics Lett. 28 (2003) 105–107. [CrossRef] [Google Scholar]
  22. C. Sulem and P.L. Sulem, The Nonlinear Schrödinger Equation, Self-Focusing and Wave Collapse. Springer-Verlag, New York, Appl. Math. Sci. (1999). [Google Scholar]
  23. J.B. Walsh, An introduction to stochastic partial differential equations, in École d'été de Probabilité de Saint-Flour, P.L. Hennequin Ed. Springer-Verlag, Berlin, Lect. Notes Math. 1180 (1986) 265–439. [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.