The periodic and open Toda lattice

Abstract

We develop algebro-geometrical approach for the open Toda lattice. For a finite Jacobi matrix we introduce a singular reducible Riemann surface and associated Baker-Akhiezer functions. We provide new explicit solution of inverse spectral problem for a finite Jacoby matrix. For the Toda lattice equations we obtain the explicit form of the equations of motion, the symplectic structure and Darboux coordinates. We develop similar approach for 2D open Toda. Explaining some the machinery we also make contact with the periodic case.

arXiv comment23 pages, Latex

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Cited by in corpus (11)

• Integrable Hierarchy of the Quantum Benjamin-Ono Equation
• On a family of KP multi-line solitons associated to rational degenerations of real hyperelliptic curves and to the finite non-periodic Toda hierarchy
• KP theory, plabic networks in the disk and rational degenerations of M--curves
• Quantum generic Toda system
• Real regular KP divisors on $\mathtt{M}$-curves and totally non-negative Grassmannians
• Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk
• An integrable system on the moduli space of rational functions and its variants
• Integrable systems whose spectral curve is the graph of a function
• Singular-boundary reductions of type-Q ABS equations
• On the open Toda chain with external forcing
• Solutions of the periodic Toda lattice via the projection procedure and by the algebra-geometric method