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We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the t−1 decay rate holds in the L → L∞ setting if the threshold energies are regular. We… (More)

We study the Cauchy problem for the $1$-d periodic fractional Schr\"odinger equation with cubic nonlinearity. In particular we prove local well-posedness in Sobolev spaces, for solutions evolving… (More)

In this paper we study fractal solutions of linear and nonlinear dispersive PDE on the torus. In the first part we answer some open questions on the fractal solutions of linear Schrödinger equation… (More)

We consider the non-selfadjoint operator H = [ −∆ + μ− V1 −V2 V2 ∆− μ+ V1 ] where μ > 0 and V1, V2 are real-valued decaying potentials. Such operators arise when linearizing a focusing NLS equation… (More)

We study the initial-boundary value problem for the derivative nonlinear Schrödinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS… (More)

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