Recursion operators, conservation laws, and integrability conditions for difference equations

DOI10.1007/s11232-011-0033-yzbMath1277.39013arXiv1004.5346OpenAlexW2063953093WikidataQ59902976 ScholiaQ59902976MaRDI QIDQ376912

Jing Ping Wang, Pavlos Xenitidis, Alexander V. Mikhailov

Publication date: 6 November 2013

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.5346

zbMATH Keywords

symmetryintegrabilityconservation lawintegrability conditionrecursion operatordifference equationAdler-Bobenko-Suris equationViallet equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Discrete version of topics in analysis (39A12)

Related Items

Perturbative symmetry approach for differential-difference equations, Characteristics of conservation laws for difference equations, Conservation laws of some lattice equations, Relations between symmetries and conservation laws for difference systems, Discrete integrable systems associated with relativistic collisions, Spectrum transformation and conservation laws of lattice potential KdV equation, Darboux transformations and recursion operators for differential-difference equations, Formal diagonalization of a discrete Lax operator and conservation laws and symmetries of dynamical systems, Second order integrability conditions for difference equations: an integrable equation, Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere, Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice, Discrete equation on a square lattice with a nonstandard structure of generalized symmetries, Determining the symmetries of difference equations, Features of Discrete Integrability, Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations ^*

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete nonlinear hyperbolic equations. Classification of integrable cases
• Symmetry approach to the integrability problem
• Extension of the module of invertible transformations. Classification of integrable systems
• Hamiltonian operators and algebraic structures related to them
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• On the integrability of homogeneous scalar evolution equations
• Lax pair for the Adler (lattice Krichever-Novikov) system
• Algebraic entropy
• Integrable systems and their recursion operators.
• The discrete Korteweg-de Vries equation
• The discrete and continuous Painlevé VI hierarchy and the Garnier systems
• Exactly integrable hyperbolic equations of Liouville type
• Cosymmetries and Nijenhuis recursion operators for difference equations
• Searching for CAC-maps
• Symmetries as integrability criteria for differential difference equations
• Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method
• Properties of Ascending Chains for Partial Difference Polynomial Systems
• INTEGRABLE LATTICE MAPS: Q_V, A RATIONAL VERSION OF Q₄
• Infinitely many conservation laws for the discrete KdV equation
• How to detect the integrability of discrete systems
• The generalized symmetry method for discrete equations
• Lenard scheme for two-dimensional periodic Volterra chain
• The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems
• Conservation laws for integrable difference equations
• Affine linear and D₄symmetric lattice equations: symmetry analysis and reductions