Semilinear Schrodinger equation: Difference between revisions

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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|well-posedness]] (both local and global)
* [[NLS wellposedness|Well-posedness]] (both local and global)
* [[NLS scattering|Scattering]] (as well as asymptotic completeness and existence of wave operators)
* [[NLS scattering|Scattering]] (as well as asymptotic completeness and existence of wave operators)
* [[NLS stability|Stability of solitons]] (orbital and asymptotic)
* [[NLS stability|Stability of solitons]] (orbital and asymptotic)

Revision as of 22:13, 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