Work

Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation

Year: 2025

Type: preprint

Abstract: We generalized the mKdV equation in order that the static equations include ${\rm sn}$ differential equation. As a result, a good correspondence was obtained between the KdV equation and the mKdV equation.For general genus two hyperelliptic curves, we obtained differential equations for Weierstrass type and Jacobi type hyperelliptic functions. Considering the special case of $λ_6=0, λ_0=0$, Weierstrass type and Jacobi type hyperelliptic functions are different solutions to the same hyperelliptic differential equations. Then these solutions are connected by the special ${\rm Sp(4, {\bf R})}$ Lie group transformation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2511.02621

Authors: Hayashi, Masahito, Shigemoto, Kazuyasu, Tsukioka, Takuya

Institutions: Osaka Institute of Technology, Bukkyo University, Tezukayama University

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416021343

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