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Toda lattice hierarchy. (English) Zbl 0577.58020
Group representations and systems of differential equations, Proc. Symp., Tokyo 1982, Adv. Stud. Pure Math. 4, 1-95 (1984).
[For the entire collection see Zbl 0566.00014.]
From the introduction: ”A hierarchy for the two-dimensional infinite Toda lattice is introduced. Its algebraic structure, the linearization, the bilinearization in terms of the \(\tau\) function, the reductions and the special solutions are investigated in detail.”
Reviewer: G.Warnecke

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)