Discrete Dubrovin equations and separation of variables for discrete systems

DOI10.1016/S0960-0779(98)00264-1zbMath1115.37349arXivsolv-int/9907015MaRDI QIDQ997430

Frank W. Nijhoff

Publication date: 6 August 2007

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9907015

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Discrete version of topics in analysis (39A12) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)

Related Items

Solutions and three-dimensional consistency for nonautonomous extended lattice Boussinesq-type equations ⋮ New hierarchies of integrable positive and negative lattice models and Darboux transformation ⋮ Hyperelliptic functions solutions of some nonlinear partial differential equations using the direct method ⋮ Closed-form modified Hamiltonians for integrable numerical integration schemes ⋮ Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps ⋮ Invariant manifolds and separation of the variables for integrable chains

Cites Work

• Discrete surfaces with constant negative Gaussian curvature and the Hirota equation.
• The spectrum of Jacobi matrices
• Darboux coordinates and Liouville-Arnold integration in loop algebras
• Separation of variables for the Ruijsenaars system
• Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions
• Theta functions and non-linear equations
• Weierstrass elliptic difference equations
• On Bäcklund transformations for many-body systems
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
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