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arXiv · 2310.14656

A graphical representation of hyperelliptic KdV solutions

Shigeki Matsutani
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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 graphically because the Riemann theta function requires several transcendental parameters. This paper presents a novel method for the graphical representation of such solutions from the algebraic treatment of the periodic and quasi-periodic solutions of the Baker-Weierstrass hyperelliptic $\wp$ functions. We demonstrate the graphical representation of the hyperelliptic $\wp$ functions of genus two.

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Shigeki Matsutani. 2023-10-23. A graphical representation of hyperelliptic KdV solutions. https://arxiv.org/abs/2310.14656

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