A numerical representation of hyperelliptic KdV solutions

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-08-05 DOI:10.1016/j.cnsns.2024.108259

引用次数: 0

Abstract

The periodic and quasi-periodic solutions of the integrable system have been studied for four decades based on the Riemann theta functions. However, there is a fundamental difficulty in representing the solutions numerically because the Riemann theta function requires several transcendental parameters. This paper presents a novel method for the numerical representation of such solutions from the algebraic treatment of the periodic and quasi-periodic solutions of the Baker–Weierstrass hyperelliptic $℘$ functions. We demonstrate the numerical representation of the hyperelliptic $℘$ functions of genus two.

查看原文本刊更多论文

超椭圆 KdV 解的数值表示

四十年来，基于黎曼θ函数对可积分系统的周期解和准周期解进行了研究。然而，由于黎曼θ 函数需要几个超越参数，因此在数值表示解方面存在根本性困难。本文从 Baker-Weierstrass 超椭圆函数周期解和准周期解的代数处理出发，提出了数值表示这类解的新方法。我们演示了属二的超椭圆函数的数值表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.