Uniformization of Jacobi varieties of trigonal curves and nonlinear differential equations

DOI10.1007/BF02482405zbMath0978.58012OpenAlexW1999731503MaRDI QIDQ5930954

Victor M. Buchstaber, Dmitry Leykin, Viktor Z.Enol'skij

Publication date: 24 July 2001

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

Full work available at URL: https://doi.org/10.1007/bf02482405

zbMATH Keywords

nonlinear differential equationsJacobi varietiestrigonal curves

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (24)

On regularization of second kind integrals ⋮ A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation ⋮ Generalised elliptic functions ⋮ Solution of the Jacobi inversion problem on non-hyperelliptic curves ⋮ Action-angle variables for the Lie-Poisson Hamiltonian systems associated with Boussinesq equation ⋮ DIFFERENTIAL STRUCTURE OF ABELIAN FUNCTIONS ⋮ Riemann theta function solutions to the coupled long wave-short wave resonance equations ⋮ THE SIGMA FUNCTION FOR WEIERSTRASS SEMIGROUPS 〈3, 7, 8〉 AND 〈6, 13, 14, 15, 16〉 ⋮ The \(\operatorname{al}\) function of a cyclic trigonal curve of genus three ⋮ Finite-band solutions for the hierarchy of coupled Toda lattices ⋮ Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy ⋮ Klein's fundamental 2-form of second kind for the \(C_{ab}\) curves ⋮ Sigma functions for telescopic curves ⋮ On one integrable system with a cubic first integral ⋮ Abelian functions for cyclic trigonal curves of genus 4 ⋮ Explicit quasi-periodic solutions of the Vakhnenko equation ⋮ Transcendental trace formulas for finite-gap potentials ⋮ Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy ⋮ Jacobi inversion on strata of the Jacobian of the \(C_{rs}\) curve \(y^r = f(x)\) ⋮ Sato Grassmannian and degenerate sigma function ⋮ Birkhoff Strata of Sato Grassmannian and Algebraic Curves ⋮ Deriving bases for abelian functions ⋮ Viktor Matveevich Buchstaber (on his 70th birthday) ⋮ Algebro-geometric solutions to the modified Sawada-Kotera hierarchy

Cites Work

• Infinite dimensional Lie algebras. An introduction
• Theta functions on Riemann surfaces
• The index of a vector field tangent to an odd-dimensional hypersurface and the signature of the relative Hessian
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