4 citations · 6 across the 3 of their papers we have counts for
7 papers · 1 filter
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…
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…