The Hamiltonian approach in classification and integrability of hydrodynamic chains

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 in corpus (7)

• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• Integrability of the Manakov--Santini hierarchy
• Differential Geometry of Hydrodynamic Vlasov Equations
• Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains
• The Kupershmidt hydrodynamic chains and lattices
• Modified dispersionless Veselov--Novikov equations and corresponding hydrodynamic chains
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions