In this paper, we consider the hyperbolic nonlinear Schr\”odinger equations
(HNLS) on $\mathbb{R}\times\mathbb{T}$. We obtain the sharp local
well-posedness up to the critical regularity for cubic nonlinearity and in
critical spaces for higher odd nonlinearities. Moreover, when the initial data
is small, we prove the global existence and scattering for the solutions to
HNLS with higher nonlinearities (except the cubic one) in critical Sobolev
spaces. The main ingredient of the proof is the sharp up to the endpoint
local/global-in-time Strichartz estimates.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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