Geometric Schrödinger-Airy Flows on Kähler Manifolds

Details Geometric Schrödinger-Airy Flows on Kähler Manifolds Geometric Schrödinger-Airy Flows on Kähler Manifolds

2012-03-02

arxiv.org/abs/1203.0549v1

Mathematics

Differential Geometry

35pages

Scientific paper

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 $S^1$ into a complete K\"ahler manifold and prove some local and global existence results.

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