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arXiv · 2410.09669

On the prolongation of a local hydrodynamic-type Hamiltonian operator to a nonlocal one

Stanislav Opanasenko·Roman O. Popovych
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Abstract

Nonlocal Hamiltonian operators of Ferapontov type are well-known objects that naturally arise local from Hamiltonian operators of Dubrovin-Novikov type with the help of three constructions, Dirac reduction, recursion scheme and reciprocal transformation. We provide an additional construction, namely the prolongation of a local hydrodynamic-type Hamiltonian operator of a subsystem to its nonlocal counterpart for the entire system. We exemplify this construction by a system governing an isothermal no-slip drift flux.

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Stanislav Opanasenko, Roman O. Popovych. 2024-10-12. On the prolongation of a local hydrodynamic-type Hamiltonian operator to a nonlocal one. https://arxiv.org/abs/2410.09669

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