Open Access
2009 Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise
Anne de Bouard, Arnaud Debussche
Author Affiliations +
Electron. J. Probab. 14: 1727-1744 (2009). DOI: 10.1214/EJP.v14-683


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.


Download Citation

Anne de Bouard. Arnaud Debussche. "Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise." Electron. J. Probab. 14 1727 - 1744, 2009.


Accepted: 24 August 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1185.35222
MathSciNet: MR2535011
Digital Object Identifier: 10.1214/EJP.v14-683

Primary: 35Q53
Secondary: 60H15 , 76B25

Keywords: central limit theorem , Korteweg-de Vries equation , solitary waves , Stochastic partial differential equations , White noise

Vol.14 • 2009
Back to Top