A third-order dispersive flow for closed curves into Kähler manifolds
arXiv:0707.2660
Abstract
This paper is devoted to studying the initial value problem for a third-order dispersive equation for closed curves into Kähler manifolds. This equation is a geometric generalization of a two-sphere valued system modeling the motion of vortex filament. We prove the local existence theorem by using geometric analysis and classical energy method.
25pages, final version