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Quasi-periodic solutions for the fourth order nonlinear Schr$\ddot{\mbox{o}}$dinger equation
GAO Meina 1,LIU Jianjun 2 *
1.College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209
2.School of Mathematics, Sichuan University, Chengdu 610065
*Correspondence author
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Funding: National Research Foundation for the Doctoral Program of Higher Education of China (No.20130181120104)
Opened online:22 May 2018
Accepted by: none
Citation: GAO Meina,LIU Jianjun.Quasi-periodic solutions for the fourth order nonlinear Schr$\ddot{\mbox{o}}$dinger equation[OL]. [22 May 2018] http://en.paper.edu.cn/en_releasepaper/content/4744994
 
 
This paper is concerned with the cubic fourth order nonlinearSchr$\ddot{\mbox{o}}$dinger equation with periodic boundary conditions$$\mathbf{i}u_t=\partial_x^4u\pm|u|^2u,\hspace{12pt}x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}.$$We show the above equation possesses Cantor families of quasi-periodic solutions of small amplitude.
Keywords:Fundamental Mathematics; Schr$\ddot{\mbox{o}}$dinger Equation; Quasi-periodic Solution
 
 
 

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