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
相关论文
共 50 条
  • [21] Homotopic mapping solution of soliton for perturbed KdV equation
    Mo Jia-Qi
    Yao Jing-Sun
    ACTA PHYSICA SINICA, 2008, 57 (12) : 7419 - 7422
  • [22] A solitary-wave solution to a perturbed KdV equation
    Allen, MA
    Rowlands, G
    JOURNAL OF PLASMA PHYSICS, 2000, 64 : 475 - 480
  • [23] Wavelet basis analysis in perturbed periodic KdV equation
    Lu, DC
    Tian, LX
    Liu, ZR
    APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 1998, 19 (11) : 1053 - 1058
  • [24] Dynamics of Traveling Waves for the Perturbed Generalized KdV Equation
    Jianjiang Ge
    Ranchao Wu
    Zengji Du
    Qualitative Theory of Dynamical Systems, 2021, 20
  • [25] Homoclinic orbits for a perturbed lattice modified KdV equation
    Rothos, VM
    THEORETICAL AND MATHEMATICAL PHYSICS, 2003, 134 (01) : 117 - 127
  • [26] Solitary Waves and Periodic Waves in a Perturbed KdV Equation
    Li, Hong
    Sun, Hongquan
    Zhu, Wenjing
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2020, 19 (03)
  • [27] Solitary Waves of the Perturbed KdV Equation with Nonlocal Effects
    Ge, Jianjiang
    Wu, Ranchao
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2023, 30 (02) : 553 - 577
  • [28] Solitary Waves and Periodic Waves in a Perturbed KdV Equation
    Hong Li
    Hongquan Sun
    Wenjing Zhu
    Qualitative Theory of Dynamical Systems, 2020, 19
  • [29] Wavelet basis analysis in perturbed periodic KdV equation
    Dianchen L.
    Lixin T.
    Zengrong L.
    Applied Mathematics and Mechanics, 1998, 19 (11) : 1053 - 1058
  • [30] Perturbed soliton solutions for an integral modified KdV equation
    Saravanan, M.
    Herman, Russell L.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 91
12345