Geometric, algebraic and analytic properties of hyperelliptic al_ab function of genus g

2026/03/11 by Shigeki Matsutani · 1 voice
Physics and Astronomy · Mathematics · #nlin.SI #math.AG

paper · pdf

arxiv published 2026/03/11 · arxiv updated 2026/04/05

Abstract

In this paper, we investigate the geometric, algebraic and analytic properties of the hyperelliptic al_ab functions of a hyperelliptic curve X with genus g as the al_ab functions together with the al_a functions are a generalization of the Jacobi elliptic sn, cn, and dn functions. We then demonstrate the differential identities of the al_ab function. These identities are the novel integrable partial nonlinear differential equations as a natural extension of the hyperelliptic solutions of the modified Korteweg-de Vries equation in terms of the al_a function. Thus, we also show that by the identities, the al_ab function has the capability to be the hyperelliptic solution to the nonlinear Schrödinger and complex modified Korteweg-de Vries equations.

Citations

• Closed real plane curves of hyperelliptic solutions of focusing gauged modified KdV equation of genus g
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• Statistical Mechanics of Non-stretching Elastica in Three Dimensional Space
• Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

Discussions

• Shigeki Matsutani: Geometric, algebraic and analytic properties of hyperelliptic $\mathrm{al}_{ab}$ function https://arxiv.org/abs/2603.10386 https://arxiv.org/pdf/2603.10386 https://arxiv.org/html/26 [bsky, 0 points, 0 comments]

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