Quasi-Periodic Solutions in a Nonlinear Schrödinger Equation

  title={Quasi-Periodic Solutions in a Nonlinear Schr{\"o}dinger Equation},
  author={Jiansheng Geng and Yingfei Yi},
Abstract In this paper, one-dimensional (1D) nonlinear Schrodinger equation i u t − u x x + m u + | u | 4 u = 0 with the periodic boundary condition is considered. It is proved that for each given constant potential m and each prescribed integer N > 1 , the equation admits a Whitney smooth family of small amplitude, time quasi-periodic solutions with N Diophantine frequencies. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method. 

Similar Papers