Instability of the Periodic Nonlinear Schr¨odinger Equation

  title={Instability of the Periodic Nonlinear Schr¨odinger Equation},
  author={Michael Christ and J. Colliander and Terence Tao},
We study the periodic non-linear Schrodinger equation −iu t +u xx = ±|u| p−1 u for initial data which are assumed to be small in some negative order Sobolev space H s (T) (s < 0), but which may have large L 2 mass. In [6], [7] these equations were shown to be ill-posed in H s (T), in the sense that the solution map was not uniformly continuous from H s (T) to itself even for short times and small norms. Here we show that these equations are even more unstable, in different ways for different p… CONTINUE READING


Publications referenced by this paper.
Showing 1-6 of 6 references

Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I . Schrodinger equations

J. Bourgain
Geom . Funct . Anal . • 1993

Solitons and the inverse scattering transform

H. Segur M. Ablowitz
SIAM Stud . Appl . Math . • 1981

The periodic nonlinear Schrodinger equation

Y. Ma M. Ablowitz
Stud . Appl . Math . • 1981

Similar Papers

Loading similar papers…