TY - JOUR
T1 - Bihamiltonian geometry and separation of variables for Toda lattices
JF - J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127
Y1 - 2001
A1 - Gregorio Falqui
A1 - Franco Magri
A1 - Marco Pedroni
PB - SISSA Library
UR - http://hdl.handle.net/1963/1354
U1 - 3101
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - A bi-Hamiltonian theory for stationary KDV flows and their separability
JF - Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52
Y1 - 2000
A1 - Gregorio Falqui
A1 - Franco Magri
A1 - Marco Pedroni
A1 - Jorge P. Zubelli
PB - SISSA Library
UR - http://hdl.handle.net/1963/1352
U1 - 3103
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy
JF - Theor. Math. Phys. 122 (2000) 17-28
Y1 - 2000
A1 - Gregorio Falqui
A1 - Franco Magri
A1 - Marco Pedroni
A1 - Jorge P. Zubelli
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/3223
U1 - 1078
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Reduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
JF - Theor. Math. Phys. 122 (2000) 176-192
Y1 - 2000
A1 - Gregorio Falqui
A1 - Franco Magri
A1 - G. Tondo
AB - We discuss the Boussinesq system with $t_5$ stationary, within a general framework for the analysis of stationary flows of n-Gel\\\'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.
PB - Springer
UR - http://hdl.handle.net/1963/3219
U1 - 1082
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - CHAP
T1 - A bihamiltonian approach to separation of variables in mechanics
T2 - 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
Y1 - 1999
A1 - Gregorio Falqui
A1 - Franco Magri
A1 - Marco Pedroni
AB - 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.
JF - 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
PB - World Scientific
UR - http://hdl.handle.net/1963/3222
U1 - 1079
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - CHAP
T1 - The method of Poisson pairs in the theory of nonlinear PDEs
T2 - 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)
Y1 - 1999
A1 - Gregorio Falqui
A1 - Franco Magri
A1 - Marco Pedroni
AB - 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.
JF - 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)
PB - Springer
UR - http://hdl.handle.net/1963/1350
U1 - 3105
U2 - Mathematics
U3 - Mathematical Physics
ER -