On Longtime Dynamics of Perturbed KdV Equations

Guan Huang

doi:10.1007/s10883-014-9238-3

On Longtime Dynamics of Perturbed KdV Equations

Guan Huang^*

^*此作品的通讯作者

Ecole Polytechnique

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

Consider a perturbed KdV equation:(Formula presented.), (Formula presented.), (Formula presented.) where the nonlinear perturbation defines analytic operators u(⋅)↦f(u(⋅)) in sufficiently smooth Sobolev spaces. Assume that the equation has an ϵ-quasi-invariant measure μ and satisfies some additional mild assumptions. Let u^ϵ(t) be a solution. Then on time intervals of order ϵ⁻¹, as ϵ→0, its actions I(u^ϵ(t,⋅)) can be approximated by solutions of a certain well-posed averaged equation, provided that the initial datum is μ-typical.

源语言	英语
页（从-至）	379-400
页数	22
期刊	Journal of Dynamical and Control Systems
卷	21
期	3
DOI	https://doi.org/10.1007/s10883-014-9238-3
出版状态	已出版 - 1 7月 2015
已对外发布	是

访问文件

10.1007/s10883-014-9238-3

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{8f5fc105faba45418f5a3efa21483e5d,

title = "On Longtime Dynamics of Perturbed KdV Equations",

abstract = "Consider a perturbed KdV equation:(Formula presented.), (Formula presented.), (Formula presented.) where the nonlinear perturbation defines analytic operators u(⋅)↦f(u(⋅)) in sufficiently smooth Sobolev spaces. Assume that the equation has an ϵ-quasi-invariant measure μ and satisfies some additional mild assumptions. Let uϵ(t) be a solution. Then on time intervals of order ϵ−1, as ϵ→0, its actions I(uϵ(t,⋅)) can be approximated by solutions of a certain well-posed averaged equation, provided that the initial datum is μ-typical.",

keywords = "Averaging, Gibbs measure, KdV, Longtime behaviour, Perturbations",

author = "Guan Huang",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2015",

month = jul,

day = "1",

doi = "10.1007/s10883-014-9238-3",

language = "English",

volume = "21",

pages = "379--400",

journal = "Journal of Dynamical and Control Systems",

issn = "1079-2724",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - On Longtime Dynamics of Perturbed KdV Equations

AU - Huang, Guan

PY - 2015/7/1

Y1 - 2015/7/1

N2 - Consider a perturbed KdV equation:(Formula presented.), (Formula presented.), (Formula presented.) where the nonlinear perturbation defines analytic operators u(⋅)↦f(u(⋅)) in sufficiently smooth Sobolev spaces. Assume that the equation has an ϵ-quasi-invariant measure μ and satisfies some additional mild assumptions. Let uϵ(t) be a solution. Then on time intervals of order ϵ−1, as ϵ→0, its actions I(uϵ(t,⋅)) can be approximated by solutions of a certain well-posed averaged equation, provided that the initial datum is μ-typical.

AB - Consider a perturbed KdV equation:(Formula presented.), (Formula presented.), (Formula presented.) where the nonlinear perturbation defines analytic operators u(⋅)↦f(u(⋅)) in sufficiently smooth Sobolev spaces. Assume that the equation has an ϵ-quasi-invariant measure μ and satisfies some additional mild assumptions. Let uϵ(t) be a solution. Then on time intervals of order ϵ−1, as ϵ→0, its actions I(uϵ(t,⋅)) can be approximated by solutions of a certain well-posed averaged equation, provided that the initial datum is μ-typical.

KW - Averaging

KW - Gibbs measure

KW - KdV

KW - Longtime behaviour

KW - Perturbations

UR - http://www.scopus.com/inward/record.url?scp=84958046044&partnerID=8YFLogxK

U2 - 10.1007/s10883-014-9238-3

DO - 10.1007/s10883-014-9238-3

M3 - Article

AN - SCOPUS:84958046044

SN - 1079-2724

VL - 21

SP - 379

EP - 400

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

IS - 3

ER -

On Longtime Dynamics of Perturbed KdV Equations

摘要

访问文件

其它文件与链接

指纹

引用此