The Mumford dynamical system and hyperelliptic Kleinian functions

DOI10.1134/s0016266323040032arXiv2402.09218OpenAlexW4393378368MaRDI QIDQ6124864

Victor M. Buchstaber

Publication date: 10 April 2024

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2402.09218

zbMATH Keywords

Korteweg-de Vries equationhyperelliptic Kleinian functionsfamily of Poisson bracketsGelfand-Dikii recursionparametric KdV hierarchy

Mathematics Subject Classification ID

Partial differential equations (35-XX)

Cites Work

• The periodic problem for the Korteweg-de Vries equation
• A Lie algebra structure in a formal variational calculation
• Birkhoff strata, Bäcklund transformations, and regularization of isospectral operators
• Sigma functions and Lie algebras of Schrödinger operators
• Heat equations in a nonholomic frame
• Parametric Korteweg-de Vries hierarchy and hyperelliptic sigma functions
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• Method for Solving the Korteweg-deVries Equation
• Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves
• σ-Functions: Old and New Results
• Integrals of nonlinear equations of evolution and solitary waves
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
• Integrable systems in the realm of algebraic geometry.
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