Article
in Modern Analysis and Applications, V. Adamyan (ed.) et al., 445-453, Oper. Theory Adv. Appl. 191, Birkhäuser, Basel, 2009 [DOI: 10.1007/978-3-7643-9921-4_27]

On the Equivalence of Different Lax Pairs for the Kac-van Moerbeke Hierarchy

Johanna Michor and Gerald Teschl

Abstract
We give a simple algebraic proof that the two different Lax pairs for the Kac-van Moerbeke hierarchy, constructed from Jacobi respectively super-symmetric Dirac-type difference operators, give rise to the same hierarchy of evolution equations. As a byproduct we obtain some new recursions for computing these equations.

MSC2000: Primary 47B36, 37K15; Secondary 81U40, 39A10
Keywords: Kac-van Moerbeke hierarchy, Lax pair, Toda hierarchy

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