Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation
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| Format: | Preprint |
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2025
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| _version_ | 1866912729238863872 |
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| author | Hayashi, Masahito Shigemoto, Kazuyasu Tsukioka, Takuya |
| author_facet | Hayashi, Masahito Shigemoto, Kazuyasu Tsukioka, Takuya |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02621 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation Hayashi, Masahito Shigemoto, Kazuyasu Tsukioka, Takuya Classical Analysis and ODEs Exactly Solvable and Integrable Systems 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. |
| title | Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation |
| topic | Classical Analysis and ODEs Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2511.02621 |