Abstract
A systematic construction of Stäckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton–Jacobi method, is derived. One-Casimir bi-Hamiltonian case is studied in details and in this case, a systematic construction of related hydrodynamic systems in arbitrary coordinates is presented, using the cofactor method and soliton symmetry constraints.
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