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Nonlinear Schrödinger equation for the twisted Laplacian. (English) Zbl 1279.35084

Summary: We establish the local well posedness of solution to the nonlinear Schrödinger equation associated to the twisted Laplacian on \(\mathbb C^n\) 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 \(A(z) = iz\), \(z \in \mathbb C\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
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