Nonlinear Schrödinger equation for the twisted Laplacian

We establish the local well posedness of solution to the nonlinear Schrödinger 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 nonlinearities including power type. The case $n=1$ represents the magnetic Schrödinger equation in the plane with magnetic potential $A(z)=iz, z\in\C$.

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