Investigation into the role of the Laurent property in integrability

DOI10.1063/1.4941370zbMath1333.39009arXiv1505.01722OpenAlexW779302405MaRDI QIDQ2795569

Takafumi Mase

Publication date: 21 March 2016

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

Full work available at URL: https://arxiv.org/abs/1505.01722

Mathematics Subject Classification ID

Group rings (16S34) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Discrete version of topics in analysis (39A12) Cluster algebras (13F60)

Related Items (17)

On the singularity structure of the discrete KdV equation ⋮ On some applications of Sakai's geometric theory of discrete Painlevé equations ⋮ Periodicity and integrability for the cube recurrence ⋮ QRT maps and related Laurent systems ⋮ Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation ⋮ Some integrable maps and their Hirota bilinear forms ⋮ Linear relations for Laurent polynomials and lattice equations ⋮ Periodicity, linearizability, and integrability in seed mutations of type AN(1) ⋮ A two-dimensional lattice equation as an extension of the Heideman–Hogan recurrence ⋮ Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice ⋮ On reductions of the Hirota-Miwa equation ⋮ On the coprimeness property of discrete systems without the irreducibility condition ⋮ Linear degree growth in lattice equations ⋮ Generators of rank 2 cluster algebras of affine types via linearization of seed mutations ⋮ Super-QRT and 4D-mappings reduced from the lattice super-KdV equation ⋮ Quivers with additive labelings: classification and algebraic entropy ⋮ Discrete Hirota reductions associated with the lattice KdV equation

Cites Work

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• Discrete integrable systems and Poisson algebras from cluster maps
• The Laurent phenomenon
• Integrability in a discrete world
• On Hirota's difference equations
• Singularity confinement for maps with the Laurent property
• Cluster algebras I: Foundations
• Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• From discrete integrable equations to Laurent recurrences
• Irreducibility and co-primeness as an integrability criterion for discrete equations
• Discrete Painlevé equations from Y-systems
• Bilinear equations and q-discrete Painlevé equations satisfied by variables and coefficients in cluster algebras
• Algebraic entropy of an extended Hietarinta–Viallet equation

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