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.

中文翻译：

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超椭圆 KdV 解的数值表示


基于黎曼 theta 函数的可积系统的周期和准周期解已经被研究了四十年。然而，用数值表示解存在根本性的困难，因为黎曼 theta 函数需要几个超越参数。本文提出了一种通过贝克-韦尔斯特拉斯超椭圆函数的周期和准周期解的代数处理来数值表示此类解的新方法。我们证明了属二超椭圆函数的数值表示。