Classification of degenerate non-homogeneous Hamiltonian operators

Abstract

In this paper, the authors 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 degenerate leading coefficient in systems of 2 and 3 components is presented.

References in corpus (2)

• Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions
• Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter-Saxton equations