A KAM Theorem for Higher Dimensional Nonlinear Schrodinger Equations

作者：Geng Jiansheng^*; You Jiangong

来源：Journal of Dynamics and Differential Equations, 2013, 25(2): 451-476.

DOI：10.1007/s10884-013-9296-3

• Schrodinger equation
• KAM tori
• Quasi-periodic solutions

We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the higher dimensional nonlinear Schrodinger equation
iu(t) - delta u + M xi u + f(vertical bar u vertical bar(2))u = 0, t is an element of R, x is an element of T-d
with periodic boundary conditions, where is a real Fourier multiplier and is a real analytic function near with . We obtain for the equation a Whitney smooth family of real-analytic small-amplitude linearly-stable quasi-periodic solutions with a nice linear normal form.

• 出版日期2013-6
• 单位南京大学