An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrodinger equation

作者：Geng Jiansheng^*; Xu Xindong; You Jiangong

来源：Advances in Mathematics, 2011, 226(6): 5361-5402.

DOI：10.1016/j.aim.2011.01.013

• Schrodinger equation
• KAM tori
• Birkhoff normal form

We prove an infinite dimensional KAM theorem. As an application, we use the theorem to study the two dimensional nonlinear Schrodinger equation
iu(t) - Delta u + vertical bar u vertical bar(2)u = 0, t is an element of R, x is an element of T(2)
with periodic boundary conditions. We obtain for the equation a Whitney smooth family of small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.

• 出版日期2011-4-1
• 单位南京大学