dorsal/arxiv
View SchemaIntegrable Systems and Isomonodromy Deformations
| Authors | Richard Beals, D. H. Sattinger |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9801010 |
| URL | https://arxiv.org/abs/solv-int/9801010 |
| DOI | 10.1016/0167-2789(93)90003-J |
| Journal | Physica D, vol 65, (1993), 17-47 |
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 $n\times n$ 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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"abstract": "We analyze in detail three classes of isomondromy deformation problems\nassociated with integrable systems. The first two are related to the scaling\ninvariance of the $n\\times n$ AKNS hierarchies and the Gel\u0027fand-Dikii\nhierarchies. The third arises in string theory as the representation of the\nHeisenberg group by $[(L^{k/n})_+,L]=I$ where $L$ is an $n^{th}$ order scalar\ndifferential operator. The monodromy data is constructed in each case; the\ninverse monodromy problem is solved as a Riemann-Hilbert problem; and a simple\nproof of the Painlev\\\u0027e property is given for the general case",
"arxiv_id": "solv-int/9801010",
"authors": [
"Richard Beals",
"D. H. Sattinger"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1016/0167-2789(93)90003-J",
"journal_ref": "Physica D, vol 65, (1993), 17-47",
"title": "Integrable Systems and Isomonodromy Deformations",
"url": "https://arxiv.org/abs/solv-int/9801010"
},
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