English

Nonlinear Schr\"{o}dinger equation for the twisted Laplacian

Analysis of PDEs 2013-04-30 v2

Abstract

We establish the local well posedness of solution to the nonlinear Schr\"{o}dinger equation associated to the twisted Laplacian on \Cn\C^n in certain first order Sobolev space. Our approach is based on Strichartz type estimates, and is valid for a general class of nonlinearities including power type. The case n=1n=1 represents the magnetic Schr\"{o}dinger equation in the plane with magnetic potential A(z)=iz,z\CA(z)=iz, z\in\C.

Keywords

Cite

@article{arxiv.1204.1843,
  title  = {Nonlinear Schr\"{o}dinger equation for the twisted Laplacian},
  author = {P. K. Ratnakumar and Vijay Kumar Sohani},
  journal= {arXiv preprint arXiv:1204.1843},
  year   = {2013}
}
R2 v1 2026-06-21T20:46:31.674Z