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Classification of integrable hydrodynamic chains and generating functions of conservation laws. (English) Zbl 1098.35097

Summary: A new approach to classification of integrable hydrodynamic chains is established. Generating functions of conservation laws are classified by the method of hydrodynamic reductions. The \(N\) parametric family of explicit hydrodynamic reductions allows us to reconstruct corresponding hydrodynamic chains. Many new hydrodynamic chains are found.

MSC:

35L40 First-order hyperbolic systems
35L65 Hyperbolic conservation laws
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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