Classification of degenerate non-homogeneous Hamiltonian operators

Marta Dell'Atti, Pierandrea Vergallo

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We investigate non-homogeneous Hamiltonian operators composed of a first order Dubrovin–Novikov operator and an ultralocal one. The study of such operators turns out to be fundamental for the inverted system of equations associated with a class of Hamiltonian scalar equations. Often, the involved operators are degenerate in the first order term. For this reason, a complete classification of the operators with a degenerate leading coefficient in systems with two and three components is presented.
Original languageEnglish
Article number033505
JournalJournal of Mathematical Physics
Issue number3
Publication statusPublished - 20 Mar 2023

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