A variational perspective on continuum limits of ABS and lattice GD equations

DOI10.3842/SIGMA.2019.044zbMath1432.37097arXiv1811.01855MaRDI QIDQ2330814

Mats Vermeeren

Publication date: 23 October 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01855

zbMATH Keywords

multidimensional consistencycontinuum limitsLagrangian multiformspluri-Lagrangian systems

Mathematics Subject Classification ID

Lattice dynamics; integrable lattice equations (37K60) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06) Integrable difference and lattice equations; integrability tests (39A36) Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K58)

Related Items (4)

A revisit to the ABS H2 equation ⋮ Quantum integrability: Lagrangian 1-form case ⋮ On the fourth-order lattice Gel'fand-Dikii equations ⋮ Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lattice equations, hierarchies and Hamiltonian structures
• On the Lagrangian structure of integrable quad-equations
• Linear integral equations and nonlinear difference-difference equations
• Lax pair for the Adler (lattice Krichever-Novikov) system
• Rational solutions to the ABS list: transformation approach
• On Hirota's difference equations
• Classification of integrable equations on quad-graphs. The consistency approach
• The discrete Korteweg-de Vries equation
• Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
• Discrete Systems and Integrability
• What is integrability of discrete variational systems?
• On the Lagrangian Structure of Integrable Hierarchies
• Discrete-time Calogero–Moser system and Lagrangian 1-form structure
• HOLOMORPHIC BUNDLES OVER ALGEBRAIC CURVES AND NON-LINEAR EQUATIONS
• The Dilogarithm Function
• Lagrangian multiforms and multidimensional consistency
• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
• Soliton solutions for ABS lattice equations: II. Casoratians and bilinearization
• The lattice Gel'fand-Dikii hierarchy
• Rational solutions to Q3 _δ in the Adler-Bobenko-Suris list and degenerations
• Linear integral equations, infinite matrices, and soliton hierarchies
• On reductions of the discrete Kadomtsev–Petviashvili-type equations
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation
• Lagrangian multiform structure for the lattice Gel'fand–Dikii hierarchy
• THE BOUSSINESQ INTEGRABLE SYSTEM: COMPATIBLE LATTICE AND CONTINUUM STRUCTURES
• Continuum limits of pluri-Lagrangian systems

This page was built for publication: A variational perspective on continuum limits of ABS and lattice GD equations