Solutions to the Hierarchy of the Periodic Toda Lattices
The hierarchy of the periodic Toda lattices is derived by means of the Appelle transformation. Members of the hierarchy are determined by equations of motion, by Hamiltonians and Lax pairs. Only two- and three-particle systems besides the basic Toda lattice are solved by quadratures in accordance with the Stäckel theorem. Other members of the hierarchy assume the solving of the polynomial equation, the degree of which is higher than four.
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