Titlebook: Lectures on Integrable Systems; Jens Hoppe Book 1992 Springer-Verlag Berlin Heidelberg 1992 Dynamische Systeme.Hamiltonian.Hamiltonian mec

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Hot-Flash

Lectures on Integrable Systems978-3-540-47274-2Series ISSN 0940-7677

LIEN

Classical Integrability of the Calogero-Moser Systems,We have seen that if one defines an . × . matrix . as . one can write the equations of motion belonging to . in the form . where . is given by

Meander

Algebraic Approach to ,, + ,/,, Interactions,Consider . Let us recall the situation for α = 0: . Without taking into account the boundary condition at 0, the eigenfunctions are . where the ..(.) are Hermite polynomials. Because of the boundary condition φ(0) = 0 only odd . (= 2. + 1) are allowed:

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凝乳

The Classical Non-Periodic Toda Lattice,Consider a system of . particles whose dynamics is governed by . (note that any interaction of the form . with . . > 0 leads to (6.1) by rescaling and shifting . . and .).

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Infinite Dimensional Toda Systems,Let us now use . → ∞ limits of gl(., ?) in the context of a concrete physical model, the periodic Toda chain:

Catheter

Differential Lax Operators,Instead of considering Lax pairs of infinite dimensional matrices (implying specific basis in vector spaces of countable dimension) one often looks at Lax equations . where . and . are differential operators of order . and ., respectively,