4 citations · 6 across the 3 of their papers we have counts for
7 papers
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 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 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…
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…
Bi-Hamiltonian aspects of the separability of the Neumann system
Marco Pedroni
The Neumann system on the 2-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian point of view on separation of variables. It is shown that, from this st…
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…