English

New Transformations for Painlev\'e's Third Transcendent

Classical Analysis and ODEs 2007-05-23 v1 Exactly Solvable and Integrable Systems

Abstract

We present transformations relating the third transcendent of Painlev\'e with parameter sets located at the corners of the Weyl chamber for the symmetry group of the system, the affine Weyl group of the root system B2(1) B^{(1)}_2 , to those at the origin. This transformation entails a scaling of the independent variable, and implies additive identities for the canonical Hamiltonians and product identities for the τ\tau-functions with these parameter sets.

Cite

@article{arxiv.math/0210019,
  title  = {New Transformations for Painlev\'e's Third Transcendent},
  author = {N. S. Witte},
  journal= {arXiv preprint arXiv:math/0210019},
  year   = {2007}
}

Comments

AMSLatex with Proc. Amer. Math. Soc. macros