English

Integrable Systems and Isomonodromy Deformations

solv-int 2009-10-31 v1 Exactly Solvable and Integrable Systems

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×nn\times n AKNS hierarchies and the Gel'fand-Dikii hierarchies. The third arises in string theory as the representation of the Heisenberg group by [(Lk/n)+,L]=I[(L^{k/n})_+,L]=I where LL is an nthn^{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

Keywords

Cite

@article{arxiv.solv-int/9801010,
  title  = {Integrable Systems and Isomonodromy Deformations},
  author = {Richard Beals and D. H. Sattinger},
  journal= {arXiv preprint arXiv:solv-int/9801010},
  year   = {2009}
}