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Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise


 
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1. Title Title of document Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise
 
2. Creator Author's name, affiliation, country Anne de Bouard; CMAP, CNRS and Ecole Polytechnique
 
2. Creator Author's name, affiliation, country Arnaud Debussche; IRMAR, ENS Cachan Bretagne
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Korteweg-de Vries equation; stochastic partial differential equations; white noise, central limit theorem; solitary waves
 
3. Subject Subject classification 35Q53; 60H15; 76B25
 
4. Description Abstract We consider a randomly perturbed Korteweg-de Vries equation. The perturbation is a random potential depending both on space and time, with a white noise behavior in time, and a regular, but stationary behavior in space. We investigate the dynamics of the soliton of the KdV equation in the presence of this random perturbation, assuming that the amplitude of the perturbation is small. We estimate precisely the exit time of the perturbed solution from a neighborhood of the modulated soliton, and we obtain the modulation equations for the soliton parameters. We moreover prove a central limit theorem for the dispersive part of the solution, and investigate the asymptotic behavior in time of the limit process.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) French ANR
 
7. Date (YYYY-MM-DD) 2009-08-24
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/683
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-683
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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