Classification of integrable hydrodynamic chains and generating functions of conservation laws

Abstract

New approach to classification of integrable hydrodynamic chains is established. Generating functions of conservation laws are classified by the method of hydrodynamic reductions. N parametric family of explicit hydrodynamic reductions allows to reconstruct corresponding hydrodynamic chains. Plenty new hydrodynamic chains are found.

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Cited by in corpus (15)

• Classical R-matrix theory for bi-Hamiltonian field systems
• Integrable (2+1)-dimensional systems of hydrodynamic type
• Integrable Dispersive Chains and Energy Dependent Schrodinger Operator
• Integrability of the Manakov--Santini hierarchy
• Differential Geometry of Hydrodynamic Vlasov Equations
• Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions
• Classification of integrable Vlasov-type equations
• Integrability, exact reductions and special solutions of the KP-Whitham equations
• Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
• Integrable pseudopotentials related to elliptic curves
• On Local Description of Two-Dimensional Geodesic Flows with a Polynomial First Integral
• Classification of integrable hydrodynamic chains
• Symmetric Matrix Ensemble and Integrable Hydrodynamic Chains
• 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