Commutator identities on associative algebras, the non-abelian Hirota difference equation and its reductions

DOI10.1134/S0040577916060039zbMath1346.37056MaRDI QIDQ314916

A. K. Pogrebkov

Publication date: 19 September 2016

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

zbMATH Keywords

reductionHirota equationcommutator identity

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Identities other than those of matrices over commutative rings (16R40) Partial difference equations (39A14)

Related Items (6)

Negative times of the Davey-Stewartson integrable hierarchy ⋮ Commutator identities and integrable hierarchies ⋮ Lie-Poisson structures over differential algebras ⋮ Symmetries of the Hirota difference equation ⋮ Higher Hirota difference equations and their reductions ⋮ Hirota difference equation and Darboux system: mutual symmetry

Cites Work

• The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
• Commutator identities on associative algebras and the integrability of nonlinear revolution equations
• Degenerative dispersion laws, motion invariants and kinetic equations
• Bäcklund transformations for the difference Hirota equation and the supersymmetric Bethe ansatz
• Resolvent approach for two-dimensional scattering problems. Application to the nonstationary Schrödinger problem and the KPI equation
• Quantum integrable models and discrete classical Hirota equations
• On Hirota's difference equations
• Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
• Hirota difference equation and a commutator identity on an associative algebra
• 2D Toda chain and associated commutator identity
• Properties of solutions of the Kadomtsev–Petviashvili I equation
• Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy
• Analytic-bilinear approach to integrable hierarchies. II. Multicomponent KP and 2D Toda lattice hierarchies
• Spin generalization of the Ruijsenaars-Schneider model, the non-Abelian 2D Toda chain, and representations of the Sklyanin algebra
• Quasideterminant solutions of a non-Abelian Hirota–Miwa equation
• On a non-Abelian Hirota–Miwa equation

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