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

Johanna Michor and Gerald Teschl

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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