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Original Articles

Bihamiltonian Geometry and Separation of Variables for Toda Lattices

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Pages 118-127 | Published online: 21 Jan 2013

References

  • Adams , M R , Harnad , J and Hurtubise , J . 1993 . Darboux Coordinates and Liouville–Arnold Integration in Loop Algebras . Comm. Math. Phys. , 155 : 385 – 413 .
  • Falqui G Magri F Pedroni M (in preparation)
  • Falqui , G , Magri , F , Pedroni , M and Zubelli , J P . 2000 . A Bi-Hamiltonian Theory for Stationary KdV Flows and Their Separability . Regular and Chaotic Dynamics , 5 : 33 – 51 .
  • Falqui , G , Magri , F and Tondo , G . 2000 . Reduction of Bihamiltonian Systems and Separation of Variables: an Example from the Boussinesq Hierarchy . Theor. Math. Phys. , 122 : 212 – 230 .
  • Flaschka , H . 1994 . “ Integrable Systems and Torus Actions ” . In Lectures on Integrable Systems , Edited by: Babelon , O . 43 – 101 . World Scientific .
  • Flaschka , H and McLaughlin , D W . 1976 . Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions . Progress Theor. Phys. , 55 : 438 – 456 .
  • Gel’fand I M Zakharevich I On the Local Geometry of a Bi-Hamiltonian Structure, in The Gel’fand Mathematical Seminars 1990–1992, Editors L Corwin et al., Birkhäuser, Boston, 1993, 51–112
  • Gel’fand I M Zakharevich I Webs, Lenard Schemes, and the Local Geometry of Bihamiltonian Toda and Lax Structures, math-ag/9903080, Selecta Mathematica (to appear)
  • Kosmann-Schwarzbach , Y and Magri , F . 1990 . Poisson–Nijenhuis Structures . Ann. Inst. Poincaré (Phys. Theor.) , 53 : 35 – 81 .
  • Kuznetsov , V B . 1997 . Separation of Variables for the D n-Type Periodic Toda Lattice . J. Phys. A , 30 : 2127 – 2138 .
  • Magri , F . 1990 . Geometry and Soliton Equations, in La Mécanique Analytique de Lagrange et son héritage . Atti Acc. Sci. Torino Suppl. , 124 : 181 – 209 .
  • Marsden , J E and Ratiu , T . 1986 . Reduction of Poisson Manifolds . Lett. Math. Phys. , 11 : 161 – 169 .
  • Meucci A The Bihamiltonian Route to the Discrete Sato Grassmannian, Ph. D. Thesis, Dipartimento di Matematica dell’Università di Milano, 1998
  • Morosi , C and Pizzocchero , L . 1996 . R-Matrix Theory, Formal Casimirs and the Periodic Toda Lattice . J. Math. Phys. , 37 : 4484 – 4513 .
  • Sklyanin E K The Quantum Toda Chain, in Nonlinear Equations in Classical and Quantum Field Theory, Meudon/Paris, 1983/1984, Lecture Notes in Phys. 226, Springer, Berlin, 1985, 196–233
  • Sklyanin , E K . 1995 . Separations of Variables: New Trends . Progr. Theor. Phys. Suppl. , 118 : 35 – 60 .

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