Geometric Schrödinger-Airy Flows on Kähler Manifolds

Abstract

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.

arXiv comment35pages

References in corpus (4)

• Global well-posedness for Schrödinger equations with derivative
• Two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions
• Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
• The derivative nonlinear Schrödinger equation on the half-line