Complete list of Darboux integrable chains of the form t1x=tx+d(t,t1)

DOI10.1063/1.3251334zbMath1236.34015arXiv0907.3785OpenAlexW3102367188MaRDI QIDQ3583624

Aslı Pekcan, Natalya A. Zheltukhina, Ismagil T. Habibullin

Publication date: 17 August 2010

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

Full work available at URL: https://arxiv.org/abs/0907.3785

zbMATH Keywords

integral equationsdifference equationsLie algebrasdifferentiationmathematical operators

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Explicit solutions, first integrals of ordinary differential equations (34A05) Ordinary differential equations of infinite order (34A35) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99) Lattice dynamics; integrable lattice equations (37K60) Ordinary lattice differential equations (34A33)

Related Items (17)

An algebraic criterion of the Darboux integrability of differential-difference equations and systems ⋮ Algebraic reductions of discrete equations of Hirota-Miwa type ⋮ On the problem of classifying integrable chains with three independent variables ⋮ On construction of Darboux integrable discrete models ⋮ On the classification of nonlinear integrable three-dimensional chains via characteristic Lie algebras ⋮ On a class of Darboux-integrable semidiscrete equations ⋮ Integrals and characteristic Lie rings of semi-discrete systems of equations ⋮ On discretization of Darboux Integrable Systems admitting second-order integrals ⋮ On structure of integrals for systems of discrete equations ⋮ Complete list of Darboux integrable chains of the form t1x=tx+d(t,t1) ⋮ Semi-discrete hyperbolic equations admitting five dimensional characteristic x-ring ⋮ Discretization of Liouville type nonautonomous equations preserving integrals ⋮ Discretization of hyperbolic type Darboux integrable equations preserving integrability ⋮ Darboux-integrable two-component nonlinear hyperbolic systems of equations ⋮ Integrability conditions for two-dimensional Toda-like equations ⋮ Characteristic Lie algebras of integrable differential-difference equations in 3D ⋮ Generalized symmetries and integrability conditions for hyperbolic type semi-discrete equations ^*

Cites Work

• The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems
• Characteristic Lie algebra and classification of semidiscrete models
• Symmetries of nonlinear hyperbolic systems of the Toda chain type
• The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane
• The discrete Korteweg-de Vries equation
• Integrable KdV systems: Recursion operators of degree four
• Non-autonomous Svinolupov-Jordan KdV systems
• Exactly integrable hyperbolic equations of Liouville type
• Symmetries as integrability criteria for differential difference equations
• Complete list of Darboux integrable chains of the form t1x=tx+d(t,t1)
• Bäcklund transformations for the sine–Gordon equations
• Integrability Conditions for n and t Dependent Dynamical Lattice Equations
• Discrete analogues of the Liouville equation
• Symmetries of systems of the hyperbolic Riccati type

This page was built for publication: Complete list of Darboux integrable chains of the form t1x=tx+d(t,t1)