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arXiv · 1203.0549

Geometric Schr\"odinger-Airy Flows on K\"ahler Manifolds

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

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Xiaowei Sun, Youde Wang. 2012-03-02. Geometric Schr\"odinger-Airy Flows on K\"ahler Manifolds. https://arxiv.org/abs/1203.0549

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