Semilinear Schrodinger equation: Difference between revisions

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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
The '''semilinear Schrodinger equation''' (NLS) is


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* [[Algebraic structure of NLS|Algebraic structure]] (Symmetries, conservation laws, transformations, Hamiltonian structure)
* [[Algebraic structure of NLS|Algebraic structure]] (Symmetries, conservation laws, transformations, Hamiltonian structure)
* [[NLS wellposedness|Local and global well-posedness theory]]
* [[NLS wellposedness|Local and global well-posedness]]
* [[NLS scattering|Scattering theory]]
* [[NLS scattering|Scattering]]
* [[NLS stability|Stability of solitons]]
* [[NLS stability|Stability of solitons]]
* [[NLS blowup|Blowup]]
* [[NLS blowup|Blowup]]

Revision as of 22:11, 5 August 2006

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