Structure of a fourth-order dispersive flow equation through the generalized Hasimoto transformation

2024/05/01 by Eiji Onodera, Onodera, Eiji · 1 citation
Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2405.00412

openalex publication_date 2024/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper focuses on a one-dimensional fourth-order nonlinear dispersive partial differential equation for curve flows on a Kähler manifold. The equation arises as a fourth-order extension of the one-dimensional Schrödinger flow equation, with physical and geometrical backgrounds. First, this paper presents a framework that can transform the equation into a system of fourth-order nonlinear dispersive partial differential-integral equations for complex-valued functions. This is achieved by developing the so-called generalized Hasimoto transformation, which enables us to handle general higher-dimensional compact Kähler manifolds. Second, this paper demonstrates the computations to obtain the explicit expression of the derived system for three examples of the compact Kähler manifolds, dealing with the complex Grassmannian as an example in detail.

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