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.

References in corpus (4)

• On integrability of (2+1)-dimensional quasilinear systems
• On the local systems Hamiltonian in the weakly nonlocal Poisson brackets
• Classical R-matrix theory of dispersionless systems: I. (1+1)-dimension theory
• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type

Cited by in corpus (12)

• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• Integrable Dispersive Chains and Energy Dependent Schrodinger Operator
• 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
• Hamiltonian Formalism of Two-Dimensional Vlasov Kinetic Equation
• Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor
• Integrable hydrodynamic chains associated with Dorfman Poisson brackets
• Classification of conservative hydrodynamic chains. Vlasov type kinetic equation, Riemann mapping and the method of symmetric hydrodynamic reductions
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions