Nonlinear equations and elliptic curves

DOI10.1007/BF02104896zbMath0595.35087MaRDI QIDQ1077629

I. M. Krichever

Publication date: 1983

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

elliptic functionszero curvature equationPeierls modelalgebro-geometric spectral theoryfinite zone solutionglobal finite-zone integrationSchrödinger difference operator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99) Elliptic functions and integrals (33E05)

Related Items

Construction of exact solutions to the Ruijsenaars–Toda lattice via generalized invariant manifolds, The Riemann problem and matrix-valued potentials with a convergent Baker-Akhiezer function, Orbits and representation of Krichever-Novikov affine-type algebras, Picard potential and Hill's equation on a torus, Holomorphic solutions of soliton equations, Whitham equations for one-phase solutions of Volterra lattice, On the problem of classifying integrable chains with three independent variables, Dubrovin method and the Toda chain, Modifications of bundles, elliptic integrable systems, and related problems, Continued fractions and periodic Jacobi matrices, The Betti map associated to a section of an abelian scheme, Computing Riemann matrices of algebraic curves, Differential Resultant, Computer Algebra and Completely Integrable Dynamical Systems, Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models, A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy, Canonically conjugate variables for the Volterra lattice with periodic boundary conditions, Statistical mechanics of nonlinear wave equations. III: Metric transitivity for hyperbolic sine-Gordon., Remarks on the local version of the inverse scattering method, The Laplace method, algebraic curves, and nonlinear equations

Cites Work

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