150 citations · 531 across the 43 of their papers we have counts for
17 papers · 1 filter
Shielding of breathers for the focusing nonlinear Schrödinger equation
Gregorio Falqui, Tamara Grava, Christian Puntini
We study a deterministic gas of breathers for the Focusing Nonlinear Schrödinger equation. The gas of breathers is obtained from a -breather solution in the limit .…
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…
The Sato Grassmannian and the CH hierarchy
G. Falqui, G. Ortenzi
We discuss how the Camassa-Holm hierarchy can be framed within the geometry of the Sato Grassmannian.
Quantisation of bending flows
Gregorio Falqui, Fabio Musso
We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in , its connection with a specific Gaudin XXX system, as…
On a Camassa-Holm type equation with two dependent variables
G. Falqui
We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced by Liu and Zhang. We briefly provide an alternative derivation o…
Gel'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited
Gregorio Falqui, Marco Pedroni
In this paper we will discuss some features of the bihamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory…
On Separation of Variables for Homogeneous SL(r) Gaudin Systems
Gregorio Falqui, Fabio Musso
By means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.
Poisson Pencils, Integrability, and Separation of Variables
Gregorio Falqui
In this paper we will review a recently introduced method for solving the Hamilton-Jacobi equations by the method of Separation of Variables. This method is based on the notion of…
A geometric approach to the separability of the Neumann-Rosochatius system
Claudio Bartocci, Gregorio Falqui, Marco Pedroni
We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are reco…
Bi-hamiltonian Geometry and Separation of Variables for Gaudin Models: a case study
Gregorio Falqui, Fabio Musso
We address the study of the classical Gaudin spin model from the bi-Hamiltonian point of view. We describe in details the sl(2) three particle case.
Gaudin Models and Bending Flows: a Geometrical Point of View
Gregorio Falqui, Fabio Musso
In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, w…
On a Poisson reduction for Gel'fand--Zakharevich manifolds
G. Falqui, M. Pedroni
We formulate and discuss a reduction theorem for Poisson pencils associated with a class of integrable systems, defined on bi-Hamiltonian manifolds, recently studied by Gel'fand an…
Separation of variables for bi-Hamiltonian systems
Gregorio Falqui, Marco Pedroni
We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special…
A note on the super Krichever map
Gregorio Falqui, Cesare Reina, Alessandro Zampa
We consider the geometrical aspects of the Krichever map in the context of Jacobian Super KP hierarchy. We use the representation of the hierarchy based on the Faa` di bruno recurs…
A Bi-Hamiltonian Theory for Stationary KdV Flows and their Separability
Gregorio Falqui, Franco Magri, Marco Pedroni +1
We present a fairly new and comprehensive approach to the study of stationary flows of the Korteweg-de Vries hierarchy. They are obtained by means of a double restriction process f…
The method of Poisson pairs in the theory of nonlinear PDEs
F. Magri, G. Falqui, M. Pedroni
The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations…
Super KP equations and Darboux transformations: another perspective on the Jacobian Super KP hierarchy
Gregorio Falqui, Cesare Reina, Alessandro Zampa
We generalize to the supersymmetric case the representation of the KP hierarchy as a set of conservation laws for the generating series of the conserved densities. We show that the…