The derivative nonlinear Schr\"odinger equation on the half line

@inproceedings{Erdougan2017TheDN,
  title={The derivative nonlinear Schr\"odinger equation on the half line},
  author={M. Burak Erdougan and T. B. Guurel and Nikolaos Tzirakis},
  year={2017}
}
We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS equation on the half line. We prove almost sharp local wellposedness, nonlinear smoothing, and small data global wellposedness in the energy space. One of the obstructions is that the crucial gauge transformation we use replaces the boundary condition with a nonlocal one. We resolve this issue by running… CONTINUE READING
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