@article {2010,
	title = {On the geometric origin of the bi-Hamiltonian structure of the Calogero-Moser system},
	journal = {Int. Math. Res. Not. (2010) 2010:279-296},
	number = {arXiv.org;0902.0953v2},
	year = {2010},
	publisher = {Oxford University Press},
	abstract = {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 pair on the cotangent bundle of gl(n,R). The relation with the Lax formalism is also discussed.},
	doi = {10.1093/imrn/rnp130},
	url = {http://hdl.handle.net/1963/3800},
	author = {Claudio Bartocci and Gregorio Falqui and Igor Mencattini and Giovanni Ortenzi and Marco Pedroni}
}
@article {2005,
	title = {Gel\\\'fand-Zakharevich Systems and Algebraic Integrability: the Volterra Lattice Revisited},
	number = {SISSA;29/2005/FM},
	year = {2005},
	abstract = {In this paper we will discuss some features of the bi-Hamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov-Novikov notion of algebro-geometric (AG) Poisson brackets.},
	doi = {10.1070/RD2005v010n04ABEH000322},
	url = {http://hdl.handle.net/1963/1689},
	author = {Gregorio Falqui and Marco Pedroni}
}
@article {2004,
	title = {A geometric approach to the separability of the Neumann-Rosochatius system},
	journal = {Differential Geom. Appl. 21 (2004) 349-360},
	number = {arXiv.org;nlin/0307021},
	year = {2004},
	abstract = {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 recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.},
	doi = {10.1016/j.difgeo.2004.07.001},
	url = {http://hdl.handle.net/1963/2541},
	author = {Claudio Bartocci and Gregorio Falqui and Marco Pedroni}
}
@article {2003,
	title = {Separation of variables for Bi-Hamiltonian systems},
	journal = {Math. Phys. Anal. Geom. 6 (2003) 139-179},
	number = {SISSA;27/2002/FM},
	year = {2003},
	publisher = {SISSA Library},
	abstract = {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 class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.},
	doi = {10.1023/A:1024080315471},
	url = {http://hdl.handle.net/1963/1598},
	author = {Gregorio Falqui and Marco Pedroni}
}
@article {2002,
	title = {On a Poisson reduction for Gel\\\'fand-Zakharevich manifolds},
	journal = {Rep.Math.Phys.50 (2002), no.3, 395},
	number = {SISSA;31/2002/FM},
	year = {2002},
	publisher = {SISSA Library},
	doi = {10.1016/S0034-4877(02)80068-4},
	url = {http://hdl.handle.net/1963/1602},
	author = {Gregorio Falqui and Marco Pedroni}
}
@article {2001,
	title = {Bihamiltonian geometry and separation of variables for Toda lattices},
	journal = {J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127},
	number = {SISSA;139/99/FM},
	year = {2001},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1354},
	author = {Gregorio Falqui and Franco Magri and Marco Pedroni}
}
@article {2000,
	title = {A bi-Hamiltonian theory for stationary KDV flows and their separability},
	journal = {Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52},
	number = {SISSA;137/99/FM},
	year = {2000},
	publisher = {SISSA Library},
	doi = {10.1070/rd2000v005n01ABEH000122},
	url = {http://hdl.handle.net/1963/1352},
	author = {Gregorio Falqui and Franco Magri and Marco Pedroni and Jorge P. Zubelli}
}
@article {2000,
	title = {An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy},
	journal = {Theor. Math. Phys. 122 (2000) 17-28},
	number = {SISSA;117/98/FM},
	year = {2000},
	publisher = {Springer},
	abstract = {We give an elementary construction of the solutions of the KP hierarchy associated with polynomial τ-functions starting with a geometric approach to soliton equations based on the concept of a bi-Hamiltonian system. As a consequence, we establish a Wronskian formula for the polynomial τ-functions of the KP hierarchy. This formula, known in the literature, is obtained very directly.},
	doi = {10.1007/BF02551166},
	url = {http://hdl.handle.net/1963/3223},
	author = {Gregorio Falqui and Franco Magri and Marco Pedroni and Jorge P. Zubelli}
}
@inbook {1999,
	title = {A bihamiltonian approach to separation of variables in mechanics},
	booktitle = {Proceedings of the workshop on nonlinearity, integrability and all that : twenty years after NEEDS \\\'79, Lecce, Italy, July 1 - 10, 1999 / ed. by M. Boiti. - Singapore : World Scientific, 2000. - p. 258-266},
	year = {1999},
	publisher = {World Scientific},
	organization = {World Scientific},
	abstract = {This paper is a report on a recent approach to the theory of separability of the Hamilton-Jacobi equations from the viewpoint of bihamiltonian geometry.},
	url = {http://hdl.handle.net/1963/3222},
	author = {Gregorio Falqui and Franco Magri and Marco Pedroni}
}
@inbook {1999,
	title = {The method of Poisson pairs in the theory of nonlinear PDEs},
	booktitle = {Direct and inverse methods in nonlinear evolution equations : Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999 / Robert Conte ... ; Antonio M. Greco ed. - Berlin : Springer, 2003. - (Lecture Notes in Physics ; 632)},
	number = {SISSA;135/99/FM},
	year = {1999},
	publisher = {Springer},
	organization = {Springer},
	abstract = {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. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation.\\nIn these lectures we touch the following subjects:\\ni) the birth and the role of the method of Poisson pairs inside the theory of the KdV equation;\\nii) the theoretical basis of the method of Poisson pairs;\\niii) the Gel\\\'fand-Zakharevich theory of integrable systems on bi-Hamiltonian manifolds;\\niv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold.\\nv) the reduction technique(s) and its use to construct classes of solutions;\\nvi) the role of the technique of separation of variables in the study of the reduced systems;\\nvii) some relations intertwining the method of Poisson pairs with the method of Lax pairs.},
	doi = {10.1007/b13714},
	url = {http://hdl.handle.net/1963/1350},
	author = {Gregorio Falqui and Franco Magri and Marco Pedroni}
}
@article {1999,
	title = {A note on fractional KDV hierarchies. II. The bihamiltonian approach},
	number = {SISSA;6/99/FM},
	year = {1999},
	publisher = {SISSA Library},
	url = {http://hdl.handle.net/1963/1220},
	author = {Paolo Casati and Gregorio Falqui and Marco Pedroni}
}
