@article{AIHPC_2007__24_2_251_0,
author = {de Bouard, A. and Debussche, A.},
title = {Random modulation of solitons for the stochastic Korteweg-de Vries equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {24},
year = {2007},
pages = {251-278},
doi = {10.1016/j.anihpc.2006.03.009},
mrnumber = {2310695},
zbl = {1158.60359},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_2_251_0}
}
de Bouard, A.; Debussche, A. Random modulation of solitons for the stochastic Korteweg-de Vries equation. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 251-278. doi : 10.1016/j.anihpc.2006.03.009. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_2_251_0/
[1] , , , Optical Solitons, Springer Series in Nonlinear Dynamics, Springer-Verlag, Berlin, 1993.
[2] , , Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981. | MR 642018 | Zbl 0472.35002
[3] , , , , Dynamics of solitons under random perturbations, Phys. Rep. 157 (1988) 63-181. | MR 920335
[4] , The stability of solitary waves, Proc. Roy. Soc. London Ser. A 328 (1972) 153-183. | MR 338584
[5] , , On the stochastic Korteweg-de Vries equation, J. Funct. Anal. 154 (1998) 215-251. | Zbl 0912.60074
[6] , , The stochastic nonlinear Schrödinger equation in , Stochastic Anal. Appl. 21 (2003) 97-126. | MR 1954077 | Zbl 1027.60065
[7] , , , White noise driven Korteweg-de Vries equation, J. Funct. Anal. 169 (1999) 532-558. | Zbl 0952.60062
[8] A. de Bouard, A. Debussche, Y. Tsutsumi, Periodic solutions of the Korteweg-de Vries equation driven by white noise, SIAM J. Math. Anal., in press. | Zbl 1075.35121
[9] , , Stochastic equations in infinite dimensions, in: Encyclopedia of Mathematics and its Application, Cambridge University Press, Cambridge, 1992. | MR 1207136 | Zbl 0761.60052
[10] , , Numerical simulation of the stochastic Korteweg-de Vries equation, Phys. D 134 (1999) 200-226. | Zbl 0948.76038
[11] , , , , Statistics of soliton-bearing systems with additive noise, Phys. Rev. E 63 (2001) 025601(R).
[12] , , Random Perturbations of Dynamical Systems, Comprehensive Studies in Mathematics, Springer-Verlag, Berlin, 1984. | MR 722136 | Zbl 0922.60006
[13] , Long-time dynamics of Korteweg-de Vries solitons driven by random perturbations, J. Statist. Phys. 105 (2001) 789-833. | Zbl 0999.35086
[14] , , , Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987) 160-197. | MR 901236 | Zbl 0656.35122
[15] , , Existence of strong solutions for Itô's stochastic equations via approximations, Probab. Theory Related Fields 105 (1996) 143-158. | MR 1392450 | Zbl 0847.60038
[16] , The stochastic, damped Korteweg-de Vries equation, J. Phys. A. 23 (1990) 1063-1084. | Zbl 0706.60068
[17] , , Nonlinear Random Waves, World Scientific, Singapore, 1994. | MR 1425880 | Zbl 1058.76500
[18] , , Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Ration. Mech. Anal. 157 (2001) 219-254. | MR 1826966 | Zbl 0981.35073
[19] , , Asymptotic stability of solitons of the subcritical gKdV equations revisited, Nonlinearity 18 (2005) 55-80. | MR 2109467 | Zbl 1064.35171
[20] , , , Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002) 347-373. | MR 1946336 | Zbl 1017.35098
[21] , The Korteweg-de Vries equation: a survey of results, SIAM Rev. 18 (1976) 412-459. | Zbl 0333.35021
[22] , , Eigenvalues, and instabilities of solitary waves, Philos. Trans. Roy. Soc. London Ser. A 340 (1992) 47-94. | MR 1177566 | Zbl 0776.35065
[23] , , Asymptotic stability of solitary waves, Comm. Math. Phys. 164 (1994) 305-349. | MR 1289328 | Zbl 0805.35117
[24] J. Printems, Aspects Théoriques et numériques de l'équation de Korteweg-de Vries stochastique, thèse, Université Paris-Sud, Orsay, France, 1998.
[25] , , , Korteweg-de Vries solitons under additive stochastic perturbations, Phys. Rev. E 58 (1998) 4166-4173.
[26] , Sur un problème non linéaire, J. Math. Pures Appl. 48 (1969) 159-172. | MR 261183 | Zbl 0187.03902
[27] , Stochastic Korteweg-de Vries equation, J. Phys. Soc. Japan 52 (1983) 2642-2648.
[28] , , Stochastic Korteweg-de Vries equation with and without damping, J. Phys. Soc. Japan 53 (1984) 3342-3350.