超椭圆函数和Kadomtsev-Petviashvili方程

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-07-08 DOI:10.1016/j.physd.2025.134819

Takanori Ayano , Victor M. Buchstaber

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引用次数: 0

摘要

本文建立了基于多维σ函数的超椭圆函数理论，得到了Kadomtsev-Petviashvili方程KP-I和KP-II的超椭圆解的显式公式。解决了一个长期存在的问题，即描述这些解与超椭圆曲线定义方程的系数变化的依赖关系，这些系数是方程的积分。

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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Hyperelliptic sigma functions and the Kadomtsev–Petviashvili equation

In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev–Petviashvili equations KP-I and KP-II are obtained. The long-standing problem of describing the dependence of these solutions on the variation of the coefficients of the defining equation of a hyperelliptic curve, which are integrals of the equations, is solved.

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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.