Invariant Tori for Benjamin-Ono Equation with Unbounded quasi-periodically forced Perturbation
Invariant Tori for Benjamin-Ono Equation with Unbounded quasi-periodically forced Perturbation
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DOI：
10.3934/dcds.2014.34.689
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发表时间：
2013-08
影响因子：
1.1
通讯作者：
Lufang Mi;K. Zhang
中科院分区：
文献类型：
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作者：
Lufang Mi;K. Zhang
本文考虑非自治Benjamin-Ono方程u_t+\mathscr{H}u_{xx}- uu_x-（F（\omega t，x，u））_x=0$$在周期边界条件下的解.利用无界扰动向量场的抽象无穷维KAM定理和部分Birkhoff规范形，证明了上述方程存在KAM环的Cantorian分支，从而存在多个时间拟周期解.
In this paper, we consider the non-autonomous Benjamin-Ono equation $$u_t+\mathscr{H}u_{xx}- uu_x- (F(\omega t,x,u))_x=0$$ under periodic boundary conditions. Using an abstract infinite dimensional KAM theorem dealing with unbounded perturbation vector-field and partial Birkhoff normal form, we will prove that there exists a Cantorian branch of KAM tori and thus many time quasi-periodic solutions for the above equation.