半离散布辛斯克方程的黎曼 Theta 函数解

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED Physica D: Nonlinear Phenomena Pub Date : 2024-12-01 Epub Date: 2024-10-10 DOI:10.1016/j.physd.2024.134398

Yaru Xu , Xianguo Geng , Yunyun Zhai

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引用次数: 0

摘要

与离散 4 × 4 矩阵谱问题相关的半离散布西内斯克方程的层次结构是通过零曲率和莱纳德递归方程推导出来的。通过半离散布森斯克层次的 Lax 矩阵的特征多项式引入了四角形曲线，并在此基础上构造了贝克-阿基泽函数、子形态函数、阿贝尔微分和黎曼 Theta 函数。最后，我们推导出半离散 Boussinesq 层次的黎曼 Theta 函数解。

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Riemann theta function solutions to the semi-discrete Boussinesq equations

The hierarchy of the semi-discrete Boussinesq equations associated with a discrete 4 × 4 matrix spectral problem has been derived by means of the zero-curvature and the Lenard recursion equations. The tetragonal curve is introduced by resorting to the characteristic polynomial of the Lax matrix for the semi-discrete Boussinesq hierarchy, upon which the Baker-Akhiezer functions, meromorphic functions, Abel differentials, and Riemann theta functions are constructed. Finally, we derive the Riemann theta function solutions to the semi-discrete Boussinesq hierarchy.

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.