S. Kuksin

most citedKhasminskii--Whitham averaging for randomly perturbed KdV equation

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2 papers

math.AP2007★ 1 cited

Khasminskii--Whitham averaging for randomly perturbed KdV equation

Sergei B. Kuksin, Andrey L. Piatnitski

We consider the damped-driven KdV equation $u ˙ - ν u_{xx} + u_{xxx} - 6 u u_{x} = ν η (t, x), x \in S^{1}, \int u d x \equiv \int η d x \equiv 0,$ where $0 < ν \leq 1$ and the random process $η$ i…

math.AP2007

KAM for the Non-Linear Schrödinger Equation

L. H. Eliasson, S. B. Kuksin

We consider the $d$ -dimensional nonlinear Schrödinger equation under periodic boundary conditions: $-i\dot u=-Δu+V(x)*u+\ep \frac{\p F}{\p \bar u}(x,u,\bar u), \quad u=u(t,x), x\in…