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

H. Aratyn; J. F. Gomes; G. V. Lobo; A. H. Zimerman

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

H. Aratyn, J. F. Gomes, G. V. Lobo, A. H. Zimerman

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.

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

with a principal gradation reduce via self-similarity limit to a polynomial Hamiltonian system of coupled Painlevé III models with four canonical variables and

affine Weyl group symmetry.

Paper Structure