Abstract
We analyze in detail three classes of isomondromy deformation problems associated with integrable systems. The first two are related to the scaling invariance of the n × n AKNS hierarchies and the Gel'fand-Dikii hierarchies. The third arises in string theory as the representation of the Heisenberg group by [(L k n ) +, L] = I where L is an nth order scalar differential operator. The monodromy data is constructed in each case; the inverse monodromy problem is solved as a Riemann-Hilbert problem; and a simple proof of the Painlevé property is given for the general case.
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