Polynomial dynamical systems and the Korteweg-de Vries equation

DOI10.1134/S0081543816060110zbMath1360.14093arXiv1605.04061OpenAlexW3101928663MaRDI QIDQ511450

Victor M. Buchstaber

Publication date: 15 February 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04061

zbMATH Keywords

Korteweg-de Vries equationpolynomial vector fieldssigma functions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Relationships between algebraic curves and integrable systems (14H70)

Related Items

Two-valued groups, Kummer varieties, and integrable billiards, Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves, Hyperelliptic sigma functions and Adler-Moser polynomials, Polynomial Lie algebras and the Zelmanov-Shalev theorem, The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications, Explicit formulas for differentiation of hyperelliptic functions, Lie algebras of heat operators in a nonholonomic frame, Almost graded current algebras on the symmetric square of a curve, Parametric Korteweg-de Vries hierarchy and hyperelliptic sigma functions, Hamiltonian operators in differential algebras, Аналитические и теоретико-числовые свойства двумерных сигма-функций, Differentiation of genus 3 hyperelliptic functions, Certain reductions of Hitchin systems of rank 2 and genera 2 and 3, Polynomial Lie algebras and growth of their finitely generated Lie subalgebras, Sigma functions and Lie algebras of Schrödinger operators, Ultraelliptic integrals and two-dimensional sigma functions, On the problem of differentiation of hyperelliptic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras
• Polynomial dynamical systems and ordinary differential equations associated with the heat equation
• Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface
• Solution of the problem of differentiation of abelian functions over parameters for families of \((n, s)\)-curves
• The periodic problem for the Korteweg-de Vries equation
• Polynomial Lie algebras
• Heat equations in a nonholomic frame
• Lax operator algebras and integrable systems
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• The Generalized Chazy Equation from the Self‐Duality Equations
• σ-Functions: Old and New Results
• Differentiation of Abelian functions with respect to parameters