Quasi-periodic solutions for the fourth order nonlinear Schr$\ddot{\mbox{o}}$dinger equation
首发时间:2018-05-22
Abstract: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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