The Hamiltonian approach in classification and integrability of hydrodynamic chains

2006/03/24 by M. V. Pavlov, Maxim V. Pavlov, Pavlov, Maxim V. · 5 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0603057

arxiv created 2006/03/24 · openalex publication_date 2006/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is considered.

Cited by

• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions
• The Kupershmidt hydrodynamic chains and lattices
• Integrability of the Manakov--Santini hierarchy
• Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains
• Classification of integrable hydrodynamic chains and generating functions of conservation laws

Related

• Integrable hydrodynamic chains associated with Dorfman Poisson brackets
• Integrability of the Gibbons--Tsarev system
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions
• The Kupershmidt hydrodynamic chains and lattices
• New Hamiltonian formalism and Lagrangian representations for integrable hydrodynamic type systems