The Painlev\'e III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable poles

@inproceedings{Guest2015ThePI,
  title={The Painlev\'e III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable poles},
  author={Martin A. Guest and Claus Hertling},
  year={2015}
}
The paper is about a Painlev\'e III equation and its relation to isomonodromic families of vector bundles on P^1 with meromorphic connections. The purpose of the paper is two-fold: it offers a conceptual language for the geometrical objects underlying Painlev\'e equations, and it offers new results on a particular Painlev\'e III equation, which we denote by P_{III}(0,0,4,-4). This is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears very widely in geometry and… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 79 REFERENCES

Novokshenov: The isomonodromic deformation method in the theory of Painlevé equations

A. R. Its, V.Yu
  • Lecture Notes in Mathematics, vol. 1191, Springer, Berlin,
  • 1986
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

Singer: Galois theory of linear differential equations

M. van der Put, M.F
  • Grundlehren der mathematischen Wissenschaften, vol. 328, Springer,
  • 2003
VIEW 2 EXCERPTS
HIGHLY INFLUENTIAL