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Motivated by the question Relationship between the vortex filament equation and the cubic Schrödinger equation, I'd like to ask the following:

Where can I find a reference on wellposedness results for the cubic Schödinger equation?

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There is quite an extensive literature on this topic:

On the one-dimensional cubic nonlinear Schrödinger equation (2010)

Global well-posedness of the cubic nonlinear Schrödinger equation on compact manifolds without boundary (2010)

Almost sure well-posedness of the cubic nonlinear Schrödinger equation (2009)

Global well-posedness for cubic nonlinear Schrödinger equation (2009)

Unconditional Uniqueness Results for the cubic Nonlinear Schrödinger Equation (2018)

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  • $\begingroup$ Thank you. Do you know of any comprehensive monograph that deals with the semilinear Schrödinger equation? $\endgroup$
    – Kei
    Commented May 16, 2019 at 22:00
  • $\begingroup$ Semilinear Schrödinger Equations: bookstore.ams.org/cln-10 $\endgroup$
    – Carlo Beenakker
    Commented May 17, 2019 at 5:36

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