| KAM Tori for the Derivative Quintic Nonlinear Schrodinger Equation |
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| 作者姓名： | Dong Feng YAN Guang Hua SHI |
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| 作者单位： | School of Mathematics and Statistics;College of Mathematics and Statistics |
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| 基金项目： | Supported by NSFC (Grant Nos. 11601487 and 11526189) |
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| 摘 要： | This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-WuJ.Math.Phys.、53,102702(2012)].
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| 关 键 词： | Derivative nonlinear Schrodinger equation KAM theorem quasi-periodic solutions BirkhofF normal form |
KAM Tori for the Derivative Quintic Nonlinear Schrödinger Equation |
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| Dong Feng YAN,Guang Hua SHI.KAM Tori for the Derivative Quintic Nonlinear Schrodinger Equation[J].Acta Mathematica Sinica,2020,36(2):153-170. |
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| Authors: | Yan Dong Feng Shi Guang Hua |
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| Institution: | 1.School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, P. R. China;2.College of Mathematics and Statistics, Hu'nan Normal University, Changsha 410006, P. R. China |
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| Abstract: | This paper is concerned with one-dimensional derivative quintic nonlinear Schrödinger equation,
iut-uxx + i(|u|4u)x=0, x ∈ T.
The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established. The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem. We mention that in the present paper the mean value of u does not need to be zero, but small enough, which is different from the assumption (1.7) in Geng-WuJ. Math. Phys., 53, 102702 (2012)]. |
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| Keywords: | Derivative nonlinear Schrödinger equation KAM theorem quasi-periodic solutions Birkhoff normal form |
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