Geometric Schrödinger-Airy Flows on Kähler Manifolds

2012/03/02 by Xiaowei Sun, Sun, Xiaowei, Youde Wang +1 · 1 citation
Mathematics · Physics and Astronomy · #35Q53 #35Q55 #37K25 #58J60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.AP #math.DG #msc:35Q53 #msc:35Q55 #msc:37K25 #msc:58J60

paper · pdf · doi:10.48550/arxiv.1203.0549

35pages

arxiv created 2012/03/02 · openalex publication_date 2012/03/02 · arxiv updated 2012/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S¹ into a complete Kähler manifold and prove some local and global existence results.

Citations

• Harmonic Mappings of Riemannian Manifolds
• Nonlinear pulse propagation in a monomode dielectric guide
• On the modulational instability of hydromagnetic waves parallel to the magnetic field

Cited by

• New Geometric Flows on Riemannian Manifolds and Applications to Schrödinger-Airy Flows

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