On long time dynamics of perturbed kdv equations

Guan HUANG YMSC,Tsinghua University

Dynamical Systems mathscidoc:2205.11008

JCDS, 21, (3), 379-400, 2014.3
Consider a perturbed KdV equation: ut +uxxx −6uux = εf(u(·)), x ∈ T = R/Z, 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.
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@inproceedings{guan2014on,
  title={ON LONG TIME DYNAMICS OF PERTURBED KDV EQUATIONS},
  author={Guan HUANG},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517135006401137210},
  booktitle={JCDS},
  volume={21},
  number={3},
  pages={379-400},
  year={2014},
}
Guan HUANG. ON LONG TIME DYNAMICS OF PERTURBED KDV EQUATIONS. 2014. Vol. 21. In JCDS. pp.379-400. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517135006401137210.
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