56 citations · 403 across the 41 of their papers we have counts for
15 papers · 1 filter
-manifolds with eventual identities, bidifferential calculus and twisted Lenard-Magri chains
Alessandro Arsie, Paolo Lorenzoni
Given an -manifold with eventual identities we examine what this structure entails from the point of view of integrable PDEs of hydrodynamic type. In particular, we show that in…
Exact Poisson pencils, -structures and topological hierarchies
Gregorio Falqui, Paolo Lorenzoni
We discuss, in the framework of Dubrovin-Zhang's perturbative approach to integrable evolutionary PDEs in 1+1 dimensions, the role of a special class of Poisson pencils, called exa…
On bi-Hamiltonian deformations of exact pencils of hydrodynamic type
Alessandro Arsie, Paolo Lorenzoni
In this paper we are interested in non trivial bi-Hamiltonian deformations of the Poisson pencil $ω_λ=ω_2+λω_1=uδ'(x-y)+\f{1}{2}u_xδ(x-y)+λδ'(x-y)$. Deformations are generated by a…
Natural connections for semi-Hamiltonian systems: The case of the -system
Paolo Lorenzoni, Marco Pedroni
Given a semi-Hamiltonian system, we construct an -manifold with a connection satisfying a suitable compatibility condition with the product. We exemplify this procedure in the c…
Reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures
Guido Carlet, Paolo Lorenzoni, Andrea Raimondo
We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner e…
Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type
John Gibbons, Paolo Lorenzoni, Andrea Raimondo
We study purely nonlocal Hamiltonian structures for systems of hydrodynamic type. In the case of a semi-Hamiltonian system, we show that such structures are related to quadratic ex…
Hamiltonian structure of reductions of the Benney system
John Gibbons, Paolo Lorenzoni, Andrea Raimondo
We show how to construct the Hamiltonian structures of any reduction of the Benney chain (dKP) starting from the family of conformal maps associated to it.
Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy
Laura Fontanelli, Paolo Lorenzoni, Marco Pedroni +1
We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy. It allows us to define a…
Flat bidifferential ideals and semihamiltonian PDEs
Paolo Lorenzoni
In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law sati…
A 3-component extension of the Camassa-Holm hierarchy
Laura Fontanelli, Paolo Lorenzoni, Marco Pedroni
We introduce a bi-Hamiltonian hierarchy on the loop-algebra of sl(2) endowed with a suitable Poisson pair. It gives rise to the usual CH hierarchy by means of a bi-Hamiltonian redu…
Metastability and dispersive shock waves in Fermi-Pasta-Ulam system
Paolo Lorenzoni, Simone Paleari
We show the relevance of the dispersive analogue of the shock waves in the FPU dynamics. In particular we give strict numerical evidences that metastable states emerging from low f…
A cohomological construction of integrable hierarchies of hydrodynamic type
Paolo Lorenzoni, Franco Magri
We explain how to use the theory of bidifferential ideals to construct integrable hierarchies of hydrodynamic type.
On the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym equations
Paolo Lorenzoni, Marco Pedroni
We show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym hierarchies can be obtained by applying a reduction process to a simple Poisson pair defined on the loo…
A bi-Hamiltonian approach to the sine-Gordon and Liouville hierarchies
Paolo Lorenzoni
In this paper we study the sine-Gordon and the Liouville hierarchies in laboratory coordinates from a bi-Hamiltonian point of view. Besides the well-known local structure these hie…
Deformations of bihamiltonian structures of hydrodynamic type
Paolo Lorenzoni
In this paper we study the deformations of bihamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems m…