English

Symmetric hyperbolic Schr\"{o}dinger equations on tori

Analysis of PDEs 2026-04-02 v1

Abstract

In this paper, we study the symmetric hyperbolic Schr\"{o}dinger equations in the periodic setting. First, we prove full range Strichartz estimates on general tori by adapting Bourgain's major arc method. The result is sharp for rational tori. Second, on two-dimensional rational tori, we establish optimal local well-posedness for two hyperbolic nonlinear Schr\"{o}dinger (HNLS) equations: the septic HNLS and the hyperbolic-elliptic Davey-Stewartson system.

Keywords

Cite

@article{arxiv.2604.00403,
  title  = {Symmetric hyperbolic Schr\"{o}dinger equations on tori},
  author = {Baoping Liu and Xu Zheng},
  journal= {arXiv preprint arXiv:2604.00403},
  year   = {2026}
}

Comments

23 pages

R2 v1 2026-07-01T11:47:29.498Z