关于带导数非线性薛定谔方程组的拟周期解（英文）  

QUASI-PERIODIC SOLUTIONS FOR THE DERIVATIVE NONLINEAR SCHRDINGER EQUATION SYSTEMS

作　　者：刘凌霞[1] 吴健[2] 

机构地区：[1]潍坊学院数学与信息科学学院,山东261061 [2]南京航空航天大学理学院,南京211106

出　　处：《南京大学学报（数学半年刊）》2014年第2期99-124,共26页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by Shandong Provincial Natural Science Foundation,China(ZR2012AM017)and(2011ZRA07006);partially supported by Jiangsu Planned Projects for Postdoctoral Research Funds(1302022C);China Postdoctoral Science Foundation funded project(2014M551583);Project supported by the National Natural Science Foundation of China(Grant NO.11401302)

摘　　要：本文中,我们考虑周期边界条件下的一维非线性薛定谔方程组{iut-uxx-i（Mξu＋｜v｜^2u）x=0,ivt-vxx-i（Mηv＋｜u｜^2v）x=0}证明了该方程组在一族小振幅,实解析,2个频率的拟周期解。In this paper,we consider one dimension nonlinear Schrodinger equation systems {iut-uxx-i（Mξu＋｜v｜^2u）x=0,ivt-vxx-i（Mηv＋｜u｜^2v）x=0} with the periodic boundary condition.We prove that the system of equations admits a whitney smooth family of small amplitude,real analytic quasi-periodic solutions with two Diophantine frequencies.The proof is based on a partial Birkhoff normal form reduction and an improved KAM method.

关 键 词：拟线性哈密顿偏微分方程 KAM定理 拟周期解 Borkhoff正规型 

分 类 号：O175[理学—数学]