Integrable Systems and Isomonodromy Deformations

Details Integrable Systems and Isomonodromy Deformations Integrable Systems and Isomonodromy Deformations

1998-01-08

arxiv.org/abs/solv-int/9801010v1

Physica D, vol 65, (1993), 17-47

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1016/0167-2789(93)90003-J

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 $n\times n$ 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 $n^{th}$ 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 Painlev\'e property is given for the general case

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