Integrability of Dirac Reduced Bi-Hamiltonian Equations

DOI10.1007/978-3-319-05254-0_2zbMath1326.35310arXiv1401.6006OpenAlexW119518475MaRDI QIDQ2948971

Alberto De Sole, Daniele Valeri, Victor G. Kac

Publication date: 7 October 2015

Published in: Trends in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.6006

zbMATH Keywords

Dirac reductionLenard-Magri schemebi-Hamiltonian equations

Mathematics Subject Classification ID

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) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Poisson algebras (17B63)

Related Items

Logarithmic vertex algebras and non-local Poisson vertex algebras, Classical and Quantum $${\mathcal {W}}$$-Algebras and Applications to Hamiltonian Equations, Erratum to: ``Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents

Cites Work

• Non-local Poisson structures and applications to the theory of integrable systems
• Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras
• Dirac reduction for Poisson vertex algebras
• Classical \(\mathcal{W}\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents
• Lie algebras and equations of Korteweg-de Vries type
• Jordan algebras and generalized Korteweg-de Vries equations
• Poisson vertex algebras in the theory of Hamiltonian equations
• Rational matrix pseudodifferential operators
• Some algebraic properties of differential operators