A collection of integrable systems of the Toda type in continuous and discrete time, with 2x2 Lax representations

Preprint English OPEN
Suris, Yuri B. (1997)
  • Subject: Nonlinear Sciences - Exactly Solvable and Integrable Systems
    arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems

A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax representation and r-matrix structure. The material is given in the "no comment" style, in particular, all proofs are omitted.
  • References (4)

    1 + h2exk −xk−1 1 + h2exk+1 −xk 1 + g e 1 + g e 1 + g e 1 + g e 1 + g2exk −xek−1 1 + g2exk+1 −xek 1 + g2exek −xek−1 1 + g2exek+1 −xek 1 + g2exk+1 −xk 1 + g2exk −xek−1 1 + g2e 1 + g2exk −xk−1 1 + g2exk+1 −xk 1 + g2exk −xek−1 1 + g2exk −xk−1 1 + ǫexk+1 −xk 1 + ǫexk −xk−1 1 + ǫexk+1 −xk 1 + ǫexk −xk−1 1 − he 1 − he • Yu.B.Suris. Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice. Physics Letters A 206 (1995) 153-161.

    • Yu.B.Suris. On some integrable systems related to the Toda lattice. J. Phys. A: Math. and Gen. 30 (1997)

    • Yu.B.Suris. A discrete-time relativistic Toda lattice. J. Phys. A: Math. and Gen. 29 (1996) 451-465.

    • Yu.B.Suris. New integrable systems related to the relativistic Toda lattice. J. Phys. A: Math. and Gen., 30 (1997) 1745-1761.

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