Derivation of Painlevé type system with $D_4^{(1)}$ affine Weyl group symmetry in a self-similarity limit

Abstract

We show how the zero-curvature equations based on a loop algebra of $D_4$ with a principal gradation reduce via self-similarity limit to a polynomial Hamiltonian system of coupled Painlevé III models with four canonical variables and $D_4^{(1)}$ affine Weyl group symmetry.

14 pages

References in corpus (1)

• Recursion operators and the hierarchies of MKdV equations related to $D_4^{(1)}$, $D_4^{(2)}$ and $D_4^{(3)}$ Kac-Moody algebras