sinh-Gordon方程谱曲线上的归一化微分

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2021-01-01 DOI:10.3934/jgm.2020023

T. Kappeler, Yannick Widmer

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引用次数: 1

摘要

环面上与sinh-Gordon方程相关的谱曲线是用方程的Lax对公式中出现的Lax算子的谱来定义的。如果谱是简单的，则它是一个无限格的开放黎曼曲面。在本文中，我们在这条曲线上构造了归一化微分，并推导了它们的零点位置的估计，这是构造角度变量所需要的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On nomalized differentials on spectral curves associated with the sinh-Gordon equation

The spectral curve associated with the sinh-Gordon equation on the torus is defined in terms of the spectrum of the Lax operator appearing in the Lax pair formulation of the equation. If the spectrum is simple, it is an open Riemann surface of infinite genus. In this paper we construct normalized differentials on this curve and derive estimates for the location of their zeroes, needed for the construction of angle variables.

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.