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arXiv · 1809.05671

KAM theorem with normal frequencies of finite limit-points for some shallow water equations

Xiaoping Yuan
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Abstract

By constructing an infinite dimensional KAM theorem of the normal frequencies being dense at finite-point, we show that some shallow water equations such as Benjamin-Bona-Mahony equation and the generalized $d$-Dim. Pochhammer-Chree equation subject to some boundary conditions possess many (a family of initial values of positive Lebesgue measure of finite dimension) smooth solutions which are quasi-periodic in time.

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Xiaoping Yuan. 2018-09-15. KAM theorem with normal frequencies of finite limit-points for some shallow water equations. https://arxiv.org/abs/1809.05671

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