%0 Journal Article %J J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127 %D 2001 %T Bihamiltonian geometry and separation of variables for Toda lattices %A Gregorio Falqui %A Franco Magri %A Marco Pedroni %B J. Nonlinear Math. Phys. 8 (2001), suppl., 118-127 %I SISSA Library %G en %U http://hdl.handle.net/1963/1354 %1 3101 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:43Z (GMT). No. of bitstreams: 1\\nnlin.SI0002008.pdf: 155961 bytes, checksum: e7c353d5acb3a321990b4309478303f5 (MD5)\\n Previous issue date: 1999 %0 Journal Article %J Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52 %D 2000 %T A bi-Hamiltonian theory for stationary KDV flows and their separability %A Gregorio Falqui %A Franco Magri %A Marco Pedroni %A Jorge P. Zubelli %B Regul. Chaotic Dyn. 5 (2000), no. 1, 33-52 %I SISSA Library %G en %U http://hdl.handle.net/1963/1352 %1 3103 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:41Z (GMT). No. of bitstreams: 1\\nnlin.SI0003020.pdf: 265442 bytes, checksum: c0f6aef68fae9d648381ca82b919ce81 (MD5)\\n Previous issue date: 1999 %R 10.1070/rd2000v005n01ABEH000122 %0 Journal Article %J Theor. Math. Phys. 122 (2000) 17-28 %D 2000 %T An elementary approach to the polynomial $\\\\tau$-functions of the KP Hierarchy %A Gregorio Falqui %A Franco Magri %A Marco Pedroni %A Jorge P. Zubelli %X 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. %B Theor. Math. Phys. 122 (2000) 17-28 %I Springer %G en_US %U http://hdl.handle.net/1963/3223 %1 1078 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-31T11:53:05Z\\nNo. of bitstreams: 1\\npolynomial.pdf: 207747 bytes, checksum: 1df27acfb336a4df11658f6c011546da (MD5) %R 10.1007/BF02551166 %0 Journal Article %J Theor. Math. Phys. 122 (2000) 176-192 %D 2000 %T Reduction of bi-Hamiltonian systems and separation of variables: an example from the Boussinesq hierarchy %A Gregorio Falqui %A Franco Magri %A G. Tondo %X 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. %B Theor. Math. Phys. 122 (2000) 176-192 %I Springer %G en_US %U http://hdl.handle.net/1963/3219 %1 1082 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-30T17:15:49Z\\nNo. of bitstreams: 1\\n9906009v1.pdf: 207707 bytes, checksum: 488733797e10a7277aa5f36438c6b2d8 (MD5) %R 10.1007/BF02551195 %0 Book Section %B 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 %D 1999 %T A bihamiltonian approach to separation of variables in mechanics %A Gregorio Falqui %A Franco Magri %A Marco Pedroni %X 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. %B 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 %I World Scientific %G en_US %U http://hdl.handle.net/1963/3222 %1 1079 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-31T10:54:51Z\\nNo. of bitstreams: 1\\n0204029v1.pdf: 382691 bytes, checksum: da8b9073eaf52cc17fa15ec8abaa1ebc (MD5) %0 Book Section %B 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) %D 1999 %T The method of Poisson pairs in the theory of nonlinear PDEs %A Gregorio Falqui %A Franco Magri %A Marco Pedroni %X 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. %B 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) %I Springer %G en %U http://hdl.handle.net/1963/1350 %1 3105 %2 Mathematics %3 Mathematical Physics %$ Made available in DSpace on 2004-09-01T12:56:39Z (GMT). No. of bitstreams: 1\\nnlin.SI0002009.pdf: 401400 bytes, checksum: dbf2efdfc64296bb0905ee82454c25c8 (MD5)\\n Previous issue date: 1999 %R 10.1007/b13714