KAM Tori for generalized Benjamin-Ono equation

Dongfeng Yan

doi:10.3934/cpaa.2015.14.941

Article Contents

2015, Volume 14, Issue 3: 941-957. Doi: 10.3934/cpaa.2015.14.941

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KAM Tori for generalized Benjamin-Ono equation

Dongfeng Yan^1,

1.
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001

Received: June 30, 2014

Revised: November 30, 2014

Published: April 2015

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Abstract

In this paper, we investigate one-dimensional generalized Benjamin-Ono equation, \begin{eqnarray} u_t+\mathcal{H}u_{xx}+u^{4}u_x=0,x\in\mathbb{T}, \end{eqnarray} and prove the existence of quasi-periodic solutions with two frequencies. The proof is based on partial Birkhoff normal form and an unbounded KAM theorem developed by Liu-Yuan[Commun.Math.Phys.307(2011)629-673].

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Mathematics Subject Classification: Primary: O175.14, O175.29.

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