Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations

@article{Christ2003AsymptoticsFM,
  title={Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations},
  author={Michael Christ and James E. Colliander and Terrence Tao},
  journal={American Journal of Mathematics},
  year={2003},
  volume={125},
  pages={1235 - 1293}
}
In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex Korteweg-de Vries (KdV) equations. Using soliton and breather solutions, they demonstrate the lack of local well-posedness for these equations below their respective endpoint regularities. In this paper, we study the defocusing analogues of these equations, namely defocusing NLS, defocusing mKdV, and real KdV, all in one… 
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