A KAM theorem for 2-dimensional nonlinear Schrodinger equations with forcing terms and(2p+1)-nonlinearities  

作　　者：Shuaishuai XUE 

机构地区：[1]School of Mathematics,Nanjing Audit University,Nanjing 211815,China

出　　处：《Frontiers of Mathematics in China》2024年第2期75-100,共26页中国高等学校学术文摘·数学（英文）

摘　　要：In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+φ_(2)(ω_(2)+t)|u|^(2p)u=0,t∈R,x∈T^(2) under periodic boundary conditions. As a result, the existence of a Whitneysmooth family of small-amplitude reducible quasi-periodic solutions is obtained.

关 键 词：Schrodinger equation reducible KAM tori small divisor quasi-periodic solution 

分 类 号：O17[理学—数学]