Semilinear Schrodinger equation

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[Many thanks to Kenji Nakanishi with valuable help with the scattering theory portion of this section. However, we are still missing many references and results, e.g. on NLS blowup. - Ed.]

The semilinear Schrodinger equation (NLS) is

for p>1. There are many specific cases of this equation which are of interest, but in this page we shall focus on the general theory. The sign choice is the defocusing case; is focussing. There are also several variants of NLS, such as NLS with potential or NLS on manifolds and obstacles; see the general page on Schrodinger equations for more discussion.

Theory

Specific semilinear Schrodinger equations