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On the Toda Lattice. II: Inverse scattering solution. (English) Zbl 0942.37505

Summary: An inverse-scattering method is developed for the solution of the exponential lattice of Toda. As an application of this method, the general \(N\)-soliton formula is derived, and constants of the motion are expressed in terms of the scattering data.
For part I see Phys. Rev. B(3) 9, 1924-1925 (1974).

MSC:

37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K60 Lattice dynamics; integrable lattice equations
82C99 Time-dependent statistical mechanics (dynamic and nonequilibrium)
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