Integrable equations and recursion operators related to the affine Lie algebras $A_r^{(1)}$

Abstract

We have derived a family of equations related to the untwisted affine Lie algebras $A_r^{(1)}$ using a Coxeter ${\mathbb{Z}}_{r+1}$ reduction. They represent the third member of the hierarchy of soliton equations related to the algebra. We also give some particular examples and impose additional reductions.

26 pages

References in corpus (1)

• Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C)

Cited by in corpus (1)

• Real Hamiltonian forms of affine Toda field theories: spectral aspects