Khasminskii--Whitham averaging for randomly perturbed KdV equation
| dc.creator | Kuksin, Sergei B. | |
| dc.creator | Piatnitski, Andrey L. | |
| dc.date | 2007-10-20 | |
| dc.date.accessioned | 2026-07-07T08:37:36Z | |
| dc.date.available | 2026-07-07T08:37:36Z | |
| dc.description | We consider the damped-driven KdV equation $$ \dot u-ν{u_{xx}}+u_{xxx}-6uu_x=\sqrtνη(t,x), x\in S^1, \int u dx\equiv \intηdx\equiv0, $$ where $0<ν\le1$ and the random process $η$ is smooth in $x$ and white in $t$. For any periodic function $u(x)$ let $ I=(I_1,I_2,...) $ be the vector, formed by the KdV integrals of motion, calculated for the potential $u(x)$. We prove that if $u(t,x)$ is a solution of the equation above, then for $0\le t\lesssimν^{-1}$ and $ν\to0$ the vector $ I(t)=(I_1(u(t,\cdot)),I_2(u(t,\cdot)),...) $ satisfies the (Whitham) averaged equation. | |
| dc.identifier | https://arxiv.org/abs/0710.3869 | |
| dc.identifier | http://arxiv.org/abs/0710.3869 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140453 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.title | Khasminskii--Whitham averaging for randomly perturbed KdV equation | |
| dc.type | text |