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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
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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Buchstaber and Mikhailov introduced the polynomial dynamical systems in $\mathbb{C}^4$ 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 deformation 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 appendix of this paper, we correct the errors.
Keywords: Abelian functions, hyperelliptic sigma functions, polynomial dynamical systems, commuting vector fields, KdV-hierarchy. 
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     author = {Takanori Ayano and Victor M. Buchstaber},
     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},
     journal = {Symmetry, integrability and geometry: methods and applications},
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Takanori Ayano; Victor M. Buchstaber. 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. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a31/

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