TY - JOUR
T1 - On Longtime Dynamics of Perturbed KdV Equations
AU - Huang, Guan
N1 - Publisher Copyright:
© 2014, Springer Science+Business Media New York.
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 - https://www.scopus.com/pages/publications/84958046044
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 -