@article{SEDP_2007-2008____A5_0, author = {de Bouard, Anne and Debussche, Arnaud}, title = {On a stochastic {Korteweg-de} {Vries} equation with homogeneous noise}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:5}, pages = {1--13}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2007-2008}, language = {en}, url = {http://www.numdam.org/item/SEDP_2007-2008____A5_0/} }
TY - JOUR AU - de Bouard, Anne AU - Debussche, Arnaud TI - On a stochastic Korteweg-de Vries equation with homogeneous noise JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:5 PY - 2007-2008 SP - 1 EP - 13 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2007-2008____A5_0/ LA - en ID - SEDP_2007-2008____A5_0 ER -
%0 Journal Article %A de Bouard, Anne %A Debussche, Arnaud %T On a stochastic Korteweg-de Vries equation with homogeneous noise %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:5 %D 2007-2008 %P 1-13 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2007-2008____A5_0/ %G en %F SEDP_2007-2008____A5_0
de Bouard, Anne; Debussche, Arnaud. On a stochastic Korteweg-de Vries equation with homogeneous noise. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2007-2008), Exposé no. 5, 13 p. http://www.numdam.org/item/SEDP_2007-2008____A5_0/
[1] T. B. Benjamin, The stability of solitary waves, Proc. Roy. Soc. London A 328 (1972), 153–183. | MR
[2] A. de Bouard, W. Craig, O. Diaz-Espinosa, P. Guyenne and C. Sulem, Long wave expansions for water waves over random topography, preprint ArXiv : 0710.0389.
[3] A. de Bouard and A. Debussche, Random modulation of solitons for the stochastic Korteweg-de Vries equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), 251–278. | Numdam | MR
[4] A. de Bouard and A. Debussche, The Korteweg-de Vries equation with multiplicative homogeneous noise, in “Stochastic Differential Equations : Theory and Applications”, P.H. Baxendale and S.V. Lototsky Ed., Interdisciplinary Math. Sciences vol. 2, World Scientific, 2007. | Zbl
[5] A. de Bouard, A. Debussche and Y. Tsutsumi, White noise driven Korteweg-de Vries equation, J. Funct. Anal. 169 (1999), 532–558. | MR | Zbl
[6] 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 (2004/2005), 815–855. | MR | Zbl
[7] A. de Bouard, E. Gautier, Exit problems related to the persistence of solitons for the Korteweg-de Vries equation with small noise, preprint ArXiv : 0801.3894.
[8] W. Craig, An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits, Comm. Partial Differential Equations 8 (1985), 787–1003. | MR | Zbl
[9] J. Garnier, Long time dynamics of Korteweg-de Vries solitons driven by random perturbations, J. stat. Phys. 105 (2001), 789–833. | MR | Zbl
[10] J. Garnier, J.C. Muñoz Grajales and A. Nachbin, Effective behaviour of solitary waves over random topography, Multiscale Model. Simul. 6 (2007), 995–1025. | MR
[11] S. Kuksin and A. Piatnitski, Khasminskii-Whitham averaging for randomly perturbed KdV equation, J. Math. Pures Appl. 89 (2008), 400–428. | MR
[12] R.L. Pego and M.I. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys. 164 (1994), 305–349. | MR | Zbl
[13] J. Printems, Aspects Théoriques et numériques de l’équation de Korteweg-de Vries stochastique, thèse, Université Paris-Sud, Orsay, France, 1998.
[14] R. Rosales and G. Papanicolaou, Gravity waves in a channel with a rough bottom, Stud. Appl. Math. 68 (1983), 89–102. | MR | Zbl
[15] M. Scalerandi, A. Romano and C.A. Condat, Korteweg-de Vries solitons under additive stochastic perturbations, Phys. Review E 58 (1998), 4166–4173.
[16] Y. Tsutsumi, Time decay of solution for the KdV equation with multiplicative space-time noise, preprint, 2007.
[17] M. Wadati, Stochastic Korteweg-de Vries equations, J. Phys. Soc. Japan 52 (1983), 2642–2648. | MR