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References

  1. F.G. Bass, Y.S. Kivshar, V.V. Konotop and Y.A. Sinitsyn. Dynamics of solitons under random perturbations. Phys. Rep. 157 (1988), 63-181. Math. Review 89a:35231
  2. T.B. Benjamin. The stability of solitary waves. Proc. Roy. Soc. London A 328 (1972), 153-183. Math. Review 49 #3348
  3. J.L. Bona, P.E. Souganidis and W. Strauss. Stability and instability of solitary waves of Korteweg-de Vries type. Proc. Roy. Soc. London A 411 (1987), 395-412. Math. Review 88m:35128
  4. A. de Bouard and A. Debussche. On the stochastic Korteweg-de Vries equation. J. Funct. Anal. 154 (1998), 215-251. Math. Review 99c:35209
  5. A. de Bouard and A. Debussche. Random modulation of solitons for the stochastic Korteweg-de Vries equation. Ann. IHP. Analyse Non linÈaire 24 (2007), 251-278. Math. Review 2008i:60103
  6. A. de Bouard and A. Debussche. The Korteweg-de Vries equation with multiplicative homogeneous noise. Stochastic Differential Equations : Theory and Applications 113-133, Interdiscip. Math. Sci., 2, World Sci. Publ., Hackensack, NJ, 2007. Math. Review 2009c:60171
  7. A. de Bouard, A. Debussche and Y. Tsutsumi. White noise driven Korteweg-de Vries equation. J. Funct. Anal. 169 (1999), 532-558. Math. Review 2000k:60125
  8. A. de Bouard, A. Debussche and Y. Tsutsumi. Periodic solutions of the Korteweg-de Vries equation driven by white noise. SIAM J. Math. Anal. 36 (2004/05), no. 3, 815--855. Math. Review 2005k:60194
  9. A. de Bouard and R. Fukuizumi. Modulation analysis for a stochastic NLS equation arising in Bose-Einstein condensation. Accepted for publication in Asymptotic Analysis. Preprint (2008) available at http://www.cmap.polytechnique.fr/preprint/
  10. A. de Bouard and E. Gautier. Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise. Accepted for publication in Discrete Contin. Dyn. Syst. Ser. A. Preprint (2008) available at http://www.cmap.polytechnique.fr/preprint/
  11. J. Frˆhlich, S. Gustafson, B. L. Jonsson and I. M. Sigal. Solitary wave dynamics in an external potential. Commun. Math. Phys. 250 (2004), 613-642. Math. Review 2005h:35320
  12. J. Frˆhlich, S. Gustafson, B. L. Jonsson and I. M. Sigal. Long time motion of NLS solitary waves in a confining potential. Ann. Henri PoincarÈ 7 (2006), 621-660. Math. Review 2007f:35269
  13. C.S. Gardner, J.M. Greene, M.D. Kruskal and R.M. Miura. Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19 (1967), 1095-1097. Math. Review number not available.
  14. J. Garnier. Asymptotic transmission of solitons through random media. SIAM J. Appl. Math. 58 (1998), 1969-1995. Math. Review 99d:35151
  15. R. Herman. The stochastic, damped Korteweg-de Vries equation. J. Phys. A. 23 (1990), 1063-1084. Math. Review 91d:35189
  16. N.V. Krylov. On the It\^o-Wentzell formula for distribution-valued processes and related topics. Preprint (2009), arXiv:0904.2752v2
  17. Y. Martel and F. Merle. Asymptotic stability of solitons of the subcritical gKdV equations revisited. Nonlinearity 18 (2005), 55-80. Math. Review 2006i:35319
  18. C. Mueller, L. Mytnik and J. Quastel. Small noise asymptotics of traveling waves. Markov Process. Related Fields 14 (2008), 333-342. MR2453698
  19. C. Mueller and R.B. Sowers. Random travelling waves for the KPP equation with noise. J. Funct. Anal. 128 (1995), 439-498. Math. Review 97a:60083
  20. R.L. Pego and M.I. Weinstein. Asymptotic stability of solitary waves. Commun. Math. Phys. 164 (1994), 305-349. Math. Review 95h:35209
  21. J. Printems. Aspects ThÈoriques et numÈriques de l'Èquation de Korteweg-de Vries stochastique. Thesis, UniversitÈ de Paris Sud, Orsay, France, 1998.
  22. M. Scalerandi, A. Romano and C.A. Condat, Korteweg-de Vries solitons under additive stochastic perturbations. Phys. Review E 58 (1998), 4166-4173. Math. Review number not available.
  23. P.C. Schuur. Asymptotic analysis of soliton problems. An inverse scattering approach. Lect. Notes in Math. 1232, Springer Verlag, Berlin, 1984. Math. Review 88e:35003
  24. M. Wadati. Stochastic Korteweg-de Vries equations. J. Phys. Soc. Japan 52 (1983), 2642-2648. Math. Review 86b:35187
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