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

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arxiv 1809.05671 v1 pith:PE5SN5UF submitted 2018-09-15 math.DS

Xiaoping Yuan This is my paper · ORCID
classification math.DS
keywords someequationequationsfinitefrequenciesnormalshallowtheorem
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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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  1. A KAM theorem for the Hamiltonian with finite zero normal frequencies and its applications

    math.DS 2019-08 conditional novelty 7.0 of 10

    For Hamiltonians with a finite number of zero normal frequencies, a KAM-type theorem states that for most frequencies the existence of invariant tori is decided by a single leftover constant, and this yields quasi-per...

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