Geometric Schrödinger-Airy flows on Kähler manifolds

We define a class of geometric flows on a complete Kähler manifold to unify some physical and mechanical models such as the motion equations of vortex filament, complex-valued mKdV equations, derivative nonlinear Schrödinger equations etc. Furthermore, we consider the existence for these flows from S 1 into a complete Kähler manifold and prove some local and global existence results.