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

Abstract

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.