Video library: V. M. Buchstaber, Hyperelliptic sigma functions and the sequence of the Novikov's $g$-equations

VIDEO LIBRARY


5th International Conference on Integrable Systems and Nonlinear Dynamics ISND-2024 October 7, 2024 10:00, Yaroslavl, IT-company "Tensor", 36 Uglichskaya str.

Hyperelliptic sigma functions and the sequence of the Novikov's $g$-equations V. M. Buchstaber^ab ^a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow ^b Centre of Integrable Systems, P.G. Demidov Yaroslavl State University
Abstract: In 1974, S. P. Novikov discovered an algebro-geometrical method for constructing periodic and quasi-periodic solutions of the KdV equation. He introduced the g-stationary equations of the KdV-hierarchy (namely the Novikov's $g$-equations) which correspond to integrable polynomial dynamical systems in $\mathbb{C}^{3g}$ with $2g$ polynomial integrals. The talk is devoted to differential equations and dynamical systems, which are integrable in hyperelliptic sigma functions. We will introduce systems of $2g$-dimensional heat equations in a nonholonomic frame which define this functions. The operators of such system generate a polynomial Lie algebra with only three generators for $g > 1$. We will construct an infinite-dimensional polynomial dynamical system that is universal for all polynomial dynamical systems corresponding to the sequence of Novikov's $g$-equations. Language: English