Local existence of a fourth order dispersive curve flow on locally hermitian symmetric spaces and the application
arXiv:1606.04664
Abstract
This paper is concerned with a fourth order nonlinear dispersive partial differential equation for closed curve flow on a Kähler manifold. The main results is that the initial value problem has a solution locally in time if the Kähler manifold is a compact locally hermitian symmetric space. The proof is based on the geometric energy method combined with a nice gauge transformation to eliminate the loss of derivatives. Interestingly, the results can be applied to construct a generalized bi-Schrödinger flow proposed by Ding and Wang. The assumption on the manifold plays a crucial role both to enjoy a good solvable structure of the problem and to reduce the generalized bi-Schrödinger flow equation to the one considered in the present paper.
arXiv comment22pages