Geometric Schr\"odinger-Airy Flows on K\"ahler Manifolds
Differential Geometry
2012-03-05 v1 Analysis of PDEs
Abstract
We define a class of geometric flows on a complete K\"ahler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equations, derivative nonlinear Schr\"odinger equations etc. Furthermore, we consider the existence for these flows from into a complete K\"ahler manifold and prove some local and global existence results.
Keywords
Cite
@article{arxiv.1203.0549,
title = {Geometric Schr\"odinger-Airy Flows on K\"ahler Manifolds},
author = {Xiaowei Sun and Youde Wang},
journal= {arXiv preprint arXiv:1203.0549},
year = {2012}
}
Comments
35pages