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 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 represents the magnetic Schr\"{o}dinger equation in the plane with magnetic potential .
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}
}