Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3
Buchstaber and Mikhailov introduced the polynomial dynamical systems in C⁴ with two polynomial integrals on the basis of commuting vector fields on the symmetric square of hyperelliptic curves. In our previous paper, we constructed the field of meromorphic functions on the sigma divisor of hyperelli...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210190 |
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| Cite this: | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 / T. Ayano, V.M. Buchstaber // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725256340307968 |
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| author | Ayano, T. Buchstaber, V.M. |
| author_facet | Ayano, T. Buchstaber, V.M. |
| citation_txt | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 / T. Ayano, V.M. Buchstaber // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Buchstaber and Mikhailov introduced the polynomial dynamical systems in C⁴ with two polynomial integrals on the basis of commuting vector fields on the symmetric square of hyperelliptic curves. In our previous paper, we constructed the field of meromorphic functions on the sigma divisor of hyperelliptic curves of genus 3 and solutions of the systems for g=3 by these functions. In this paper, as an application of our previous results, we construct two parametric deformations of the KdV hierarchy. This new system is integrated in the meromorphic functions on the sigma divisor of hyperelliptic curves of genus 3. In Section 8 of our previous paper [Funct. Anal. Appl. 51 (2017), 162-176], there are miscalculations. In the appendix of this paper, we correct the errors.
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| first_indexed | 2025-12-07T21:24:41Z |
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| id | nasplib_isofts_kiev_ua-123456789-210190 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:41Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
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| spelling | Ayano, T. Buchstaber, V.M. 2025-12-03T14:31:56Z 2019 Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 / T. Ayano, V.M. Buchstaber // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14K25; 14H40; 14H42; 14H70 arXiv: 1811.07138 https://nasplib.isofts.kiev.ua/handle/123456789/210190 https://doi.org/10.3842/SIGMA.2019.032 Buchstaber and Mikhailov introduced the polynomial dynamical systems in C⁴ with two polynomial integrals on the basis of commuting vector fields on the symmetric square of hyperelliptic curves. In our previous paper, we constructed the field of meromorphic functions on the sigma divisor of hyperelliptic curves of genus 3 and solutions of the systems for g=3 by these functions. In this paper, as an application of our previous results, we construct two parametric deformations of the KdV hierarchy. This new system is integrated in the meromorphic functions on the sigma divisor of hyperelliptic curves of genus 3. In Section 8 of our previous paper [Funct. Anal. Appl. 51 (2017), 162-176], there are miscalculations. In the appendix of this paper, we correct the errors. The authors are grateful to Shigeki Matsutani for pointing out the relations between his paper [12] and our results in this paper, and for valuable comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 Article published earlier |
| spellingShingle | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 Ayano, T. Buchstaber, V.M. |
| title | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 |
| title_full | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 |
| title_fullStr | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 |
| title_full_unstemmed | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 |
| title_short | Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3 |
| title_sort | construction of two parametric deformation of kdv-hierarchy and solution in terms of meromorphic functions on the sigma divisor of a hyperelliptic curve of genus 3 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210190 |
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