丛洪滋

493

  • 教授     博士生导师   硕士生导师
  • 性别:男
  • 毕业院校:复旦大学
  • 学位:博士
  • 所在单位:数学科学学院
  • 学科:应用数学
  • 办公地点:创新园大厦B1211
  • 电子邮箱:conghongzi@dlut.edu.cn

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开通时间:2025.3.31

最后更新时间:2025.3.31

ON THE EXISTENCE OF FULL DIMENSIONAL KAM TORUS FOR NONLINEAR SCHRODINGER EQUATION

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论文类型:期刊论文

发表时间:2019-11-01

发表刊物:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

收录刊物:SCIE

卷号:39

期号:11

页面范围:6599-6630

ISSN号:1078-0947

关键字:KAM theory; almost periodic solution; Gevrey space; nonlinear Schrodinger equation

摘要:In this paper, we study the following nonlinear Schrodinger equation
   root-1u(t) - u(xx) + V * u + epsilon f (x)vertical bar u vertical bar(4)u = 0, x is an element of T = R/2 pi Z, (1)
   where V * is the Fourier multiplier defined by <((V * u))over cap>(n) = V-n(u) over cap (n), V-n is an element of [-1, 1] and f (x) is Gevrey smooth. It is shown that for 0 <= vertical bar epsilon vertical bar << 1, there is some (V-n)(n is an element of Z) such that, the equation (1) admits a time almost periodic solution (i.e., full dimensional KAM torus) in the Gevrey space. This extends results of Bourgain [7] and Cong-Liu-Shi-Yuan [8] to the case that the nonlinear perturbation depends explicitly on the space variable x. The main difficulty here is the absence of zero momentum of the equation.