Poisson algebras associated with constrained dispersionless modified Kadomtsev–Petviashvili hierarchies

DOI10.1063/1.1322080zbMath1004.37045arXivnlin/0001036OpenAlexW1873393476MaRDI QIDQ2731824

Jen-Hsu Chang, Ming-Hsien Tu

Publication date: 30 July 2001

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

Full work available at URL: https://arxiv.org/abs/nlin/0001036

zbMATH Keywords

Lax representationbi-Hamiltonian structuresPoisson algebrasDirac reductionKadomtsev-Petviashvili hierarchiesfree-field realizationsKupershmidt-Wilson theorem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Poisson algebras (17B63)

Cites Work

• On the Benney equations
• Modifying Lax equations and the second Hamiltonian structure
• Classical \(W\)-algebras
• The dispersionless Lax equations and topological minimal models
• Constrained KP hierarchy and bi-Hamiltonian structures
• An \(r\)-matrix approach to nonstandard classes of integrable equations
• Poisson structures for dispersionless integrable systems and associated \(W\)-algebras
• Classical \(r\)-matrices and compatible Poisson structures for Lax equations on Poisson algebras
• A note on the Poisson brackets associated with Lax operators
• Mathematics of dispersive water waves
• On the Miura Map between the dispersionless KP and dispersionless modified KP hierarchies
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies

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