53 citations · 372 across the 38 of their papers we have counts for
39 papers
Miura-reciprocal transformations and localizable Poisson pencils
P. Lorenzoni, S. Shadrin, R. Vitolo
We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain…
Projective geometry of homogeneous second order Hamiltonian operators
Pierandrea Vergallo, Raffaele Vitolo
We prove the invariance of homogeneous second-order Hamiltonian operators under the action of projective reciprocal transformations. We establish a correspondence between such oper…
WDVV equations: Hamiltonian operators and symbolic computations
Jakub Vašíček, Raffaele Vitolo
We describe software for symbolic computations that we developed in order to find Hamiltonian operators for Witten--Dijkgraaf--Verlinde--Verlinde (WDVV) equations, and verify their…
WDVV equations and invariant bi-Hamiltonian formalism
Jakub Vašíček, Raffaele Vitolo
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for . More example…
Weakly nonlocal Poisson brackets: tools, examples, computations
Matteo Casati, Paolo Lorenzoni, Daniele Valeri +1
We implement an algorithm for the computation of Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems: Maple, Reduce and Mathematic…
Classification of bi-Hamiltonian pairs extended by isometries
Maxim V. Pavlov, Pierandrea Vergallo, Raffaele Vitolo
The aim of this article is to classify pairs of first-order Hamiltonian operators of Dubrovin-Novikov type such that one of them has a non-local part defined by an isometry of its…