A graphical representation of hyperelliptic KdV solutions

Author:

Shigeki Matsutani

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Algebraic Geometry (math.AG)

journal:

date:

2023-10-22 16:00:00

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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