Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
Solitary waves of generalized Kadomtsev-Petviashvili equations
On a stochastic Korteweg-de Vries equation with homogeneous noise
Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations
We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non degenerate,...
Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
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