58 citations · 284 across the 27 of their papers we have counts for
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Poisson quasi-Nijenhuis deformations of the canonical PN structure
Gregorio Falqui, Igor Mencattini, Marco Pedroni
We present a result which allows us to deform a Poisson-Nijenhuis manifold into a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Under an additional assumption, the…
Poisson quasi-Nijenhuis manifolds and the Toda system
G. Falqui, I. Mencattini, G. Ortenzi +1
The notion of Poisson quasi-Nijenhuis manifold generalizes that of Poisson-Nijenhuis manifold. The relevance of the latter in the theory of completely integrable systems is well es…
On the Geometry of Extended Self-Similar Solutions of the Airy Shallow Water Equations
Roberto Camassa, Gregorio Falqui, Giovanni Ortenzi +1
Self-similar solutions of the so called Airy equations, equivalent to the dispersionless nonlinear Schrödinger equation written in Madelung coordinates, are found and studied from…
Poisson pencils: reduction, exactness, and invariants
Paolo Lorenzoni, Marco Pedroni, Andrea Raimondo
We study the invariants (in particular, the central invariants) of suitable Poisson pencils from the point of view of the theory of bi-Hamiltonian reduction, paying a particular at…
On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system
C. Bartocci, G. Falqui, I. Mencattini +2
We show that the bi-Hamiltonian structure of the rational n-particle (attractive) Calogero-Moser system can be obtained by means of a double projection from a very simple Poisson p…
On the Bi-Hamiltonian Theory for the Harry Dym Equation
Marco Pedroni, Vincenzo Sciacca, Jorge P. Zubelli
We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg-de Vries equation and other soliton equations. This is achieved by means of a cer…