University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Exit times and persistence of solitons for a stochastic Korteweg-de Vries Equation

Exit times and persistence of solitons for a stochastic Korteweg-de Vries Equation

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Stochastic Partial Differential Equations (SPDEs)

Solitons constitute a two parameters family of particular solution to the Korteweg-de Vries (KdV) equation. They are progressive localized waves that propagate with constant speed and shape. They are stable in many ways against perturbations or interactions. We consider the stability with respect to random perturbations by an additive noise of small amplitude. It has been proved by A. de Bouard and A. Debussche that originating from a soliton profile, the solution remains close to a soliton with randomly fluctuating parameters. We revisit exit times from a neighborhood of the deterministic soliton and randomly fluctuating solitons using large deviations. This allows to quantify the time scales on which such approximations hold and the gain obtained by eliminating secular modes in the study of the stability.

This talk is part of the Isaac Newton Institute Seminar Series series.

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