Classification of three-dimensional integrable scalar discrete equations

DOI10.1007/s11005-008-0230-2zbMath1153.37432arXiv0706.2464OpenAlexW2119458225MaRDI QIDQ934989

B. E. Eshmatov, Xianqiang Yang

Publication date: 31 July 2008

Published in: Letters in Mathematical Physics, Programming and Computer Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.2464

zbMATH Keywords

numerical examplesintegrable systemscomputer algebrafirst integralsdiscrete equationscomputer algebra programlarge sparse systemsLax pairlinear algebraic systemsoverdetermined systemsrational coefficientslarge polynomial systemsLinear Selective Systems Solvernon-abelian Laurent ordinary differential equationsymmetry investigation

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Symbolic computation and algebraic computation (68W30) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Direct numerical methods for linear systems and matrix inversion (65F05) Packaged methods for numerical algorithms (65Y15) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04)

Related Items (5)

Symbolic computation of Lax pairs of partial difference equations using consistency around the cube ⋮ Classification of three-dimensional integrable scalar discrete equations ⋮ Non-commutative generalization of integrable quadratic ODE systems ⋮ Multi-component extension of CAC systems ⋮ Consistency on cubic lattices for determinants of arbitrary orders

Uses Software

• LinBox
• Maple
• REDUCE
• streamsolve.red
• CRACK
• FORM

Cites Work

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• Discrete nonlinear hyperbolic equations. Classification of integrable cases
• Classification of three-dimensional integrable scalar discrete equations
• Integrable evolution equations on associative algebras
• Integrable ODEs on associative algebras
• Classification of integrable equations on quad-graphs. The consistency approach
• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• On organizing principles of discrete differential geometry. Geometry of spheres
• An algebraic formula for superposition and the completeness of the Bäcklund transformations of (2+1)-dimensional integrable systems
• An Integrable Discretization of a 2+1‐dimensional Sine‐Gordon Equation
• Reciprocal Figures, Graphical Statics, and Inversive Geometry of the Schwarzian BKP Hierarchy

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