Nonuniqueness of Weak Solutions of the Nonlinear Schrödinger Equation

@inproceedings{Christ2005NonuniquenessOW,
  title={Nonuniqueness of Weak Solutions of the Nonlinear Schr{\"o}dinger Equation},
  author={Michael Christ},
  year={2005}
}
Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schrödinger equation, with cubic or quadratic nonlinearities, are not unique. For any s < 0 there exist nonzero generalized solutions varying continuously in the Sobolev space H, with identically vanishing initial data. 

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