Khasminskii-Whitham averaging for randomly perturbed KdV equation

被引：32
|
作者：
Kuksin, Sergei B. [1 ,2 ]
Piatnitski, Andrey L. [3 ,4 ]
机构：
[1] Ecole Polytech, CMLS, F-91128 Palaiseau, France
[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland
[3] Narvik Univ Coll, N-8505 Narvik, Norway
[4] RAS, PN Lebedev Phys Inst, Moscow 119991, Russia
来源：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2008年 / 89卷 / 04期
关键词：
D O I：
10.1016/j.matpur.2007.12.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the damped-driven KdV equation: [GRAPHICS] where 0 < v < 1 and the random process eta 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 <= t less than or similar to v(-1) and v -> 0 the vector I(t) = (I-1(u(t,.)), I-2(u(t,.)), . . . ) satisfies the (Whitham) averaged equation. (c) 2007 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码：400 / 428
页数：29
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