Second order integrability conditions for difference equations: an integrable equation

DOI10.1007/s11005-013-0668-8zbMath1305.39011arXiv1305.4347OpenAlexW3105597154WikidataQ61835377 ScholiaQ61835377MaRDI QIDQ464330

Pavlos Xenitidis, Alexander V. Mikhailov

Publication date: 17 October 2014

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4347

zbMATH Keywords

symmetryconservation lawintegrability conditionrecursion operatorLax pairdifference equationBogoyavlensky lattice

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Partial difference equations (39A14)

Related Items (19)

Singularity analysis and bilinear approach to some Bogoyavlensky equations ⋮ Symmetries of ${\mathbb{Z}}_{N}$ graded discrete integrable systems ⋮ On a special coupled lattice system of the discrete Boussinesq type ⋮ Classification of five-point differential–difference equations II ⋮ Classification of five-point differential-difference equations ⋮ On the integrability of lattice equations with two continuum limits ⋮ On integrability of a discrete analogue of Kaup - Kupershmidt equation ⋮ Discrete equation on a square lattice with a nonstandard structure of generalized symmetries ⋮ Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations ⋮ Self-dual systems, their symmetries and reductions to the Bogoyavlensky lattice ⋮ Darboux transformations with tetrahedral reduction group and related integrable systems ⋮ On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations ⋮ Determining the symmetries of difference equations ⋮ Integrable modifications of the Ito-Narita-Bogoyavlensky equation ⋮ Algebraic entropy of a class of five-point differential-difference equations ⋮ ${{\mathbb{Z}}_{N}}$ graded discrete Lax pairs and integrable difference equations ⋮ On consistent systems of difference equations ⋮ A discrete Darboux-Lax scheme for integrable difference equations ⋮ Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations ^*

Cites Work

• Unnamed Item
• Unnamed Item
• Recursion operators, conservation laws, and integrability conditions for difference equations
• Classification of integrable equations on quad-graphs. The consistency approach
• A new recursion operator for Adler's equation in the Viallet form
• Generalized symmetry integrability test for discrete equations on the square lattice
• Cosymmetries and Nijenhuis recursion operators for difference equations
• Differential–difference equations associated with the fractional Lax operators
• Toward a theory of integrable hyperbolic equations of third order
• Generalized symmetry classification of discrete equations of a class depending on twelve parameters
• On some class of reductions for the Itoh–Narita–Bogoyavlenskii lattice
• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
• Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice
• Affine linear and D₄symmetric lattice equations: symmetry analysis and reductions

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