Classical \(r\)-matrices and compatible Poisson structures for Lax equations on Poisson algebras
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Publication:1809288
DOI10.1007/s002200050626zbMath0949.37053arXivmath-ph/0506029OpenAlexW1995146086MaRDI QIDQ1809288
Publication date: 16 December 1999
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math-ph/0506029
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Poisson manifolds; Poisson groupoids and algebroids (53D17)
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Transposed BiHom-Poisson algebras ⋮ R-MATRICES AND HAMILTONIAN STRUCTURES FOR CERTAIN LAX EQUATIONS ⋮ Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy ⋮ Lie algebras with quadratic dimension equal to 2 ⋮ Poisson structures on finitary incidence algebras ⋮ -(bi)derivations and transposed Poisson algebra structures on Lie algebras ⋮ Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras ⋮ Nonlocal hydrodynamic type of equations ⋮ Dispersionless integrable equations as coisotropic deformations: extensions and reductions ⋮ Recursion operator for a system with non-rational Lax representation ⋮ Poisson bialgebras ⋮ Additional symmetries and Bäcklund transformations for the dispersionless Harry Dym hierarchy ⋮ Poisson algebras associated with constrained dispersionless modified Kadomtsev–Petviashvili hierarchies ⋮ On the dispersionless Dym hierarchy of hydrodynamic type: two approaches ⋮ On the Miura Map between the dispersionless KP and dispersionless modified KP hierarchies ⋮ On extension of classical Baer results to Poisson algebras ⋮ Coisotropic deformations of associative algebras and dispersionless integrable hierarchies ⋮ Dispersionless noncommutative Kadomtsev-Petviashvili hierarchy: multi-Hamiltonian structure and large N-like V-algebras ⋮ The WDVV symmetries in two-primary models ⋮ New extension of dispersionless Harry Dym hierarchy ⋮ Gauge Transformation and Reciprocal Link for (2+1)-Dimensional Integrable Field Systems ⋮ The algebraic classification and degenerations of nilpotent Poisson algebras ⋮ Recursion operator and dispersionless rational Lax representation ⋮ Classical \(R\)-matrices on Poisson algebras and related dispersionless systems
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