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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 58 open journal systems 


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

Anne de Bouard, CMAP, CNRS and Ecole Polytechnique
Arnaud Debussche, IRMAR, ENS Cachan Bretagne


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.


Full text: PDF

Pages: 1727-1744

Published on: August 24, 2009
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Electronic Journal of Probability. ISSN: 1083-6489