We prove new local and global well-posedness results for the cubic one-dimensional Nonlinear Schr\"odinger Equation in Modulation Spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved quantities from the integrability of the equation, persistence of regularity and by separating off the time evolution of finitely many Picard iterates.
Pseudodifferential operators on $L^p$, Wiener amalgam and modulation spaces
On the Schrödinger equation with potential in modulation spaces
Some new well-posedness results for the Klein-Gordon-Schrödinger system
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