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

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*

Download