Hyperbolic nonlinear Schrödinger equations on ℝ× \mathbbT

2025/04/22 by Engin Başakoğlu, Chenmin Sun, Başakoğlu, Engin +5 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2504.15836

openalex publication_date 2025/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

In this paper, we consider the hyperbolic nonlinear Schrödinger equations (HNLS) on ℝ×\mathbbT. 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.

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Cited by

• Strichartz estimates for the generalized Zakharov-Kuznetsov equation on ℝ × \mathbbT and applications

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