Non linear Schrödinger equation for the twisted Laplacian

Details Non linear Schrödinger equation for the twisted Laplacian Non linear Schrödinger equation for the twisted Laplacian

2012-04-09

arxiv.org/abs/1204.1843v1

Mathematics

Analysis of PDEs

Scientific paper

We establish the local well posedness of solution to the non-linear Schr\"{o}dinger equation associated to the twisted Laplacian on $\C^n$ in certain first order Sobolev space. Our approach is based on Strichartz type estimates, and is valid for a general class of non linearities including power type. The case $n=1$ represents the magnetic Schr\"{o}dinger equation in the plane with magnetic potential $A(z)=iz, z\in\C$.

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