Multiple instantons representing higher-order Chern-Pontryagin classes

It has been shown in the work of Chakrabarti, Sherry and Tchrakian that the chiral SO_±(4p) Yang-Mills theory in the Euclidean 4p (p ≥ 2) dimensions allows an axially symmetric self-dual system of equations similar to Witten's instanton equations in the classical 4-dimensional SU(2) ∼ SO_±(4) theory and the solutions represent a new class of instantons. However the rigorous existence of these higher-dimensional instanton solutions has remained open except for the solution of unit charge representing a single instanton. In this paper we establish an existence and uniqueness theorem for multi-instantons of arbitrary charges in the case p ≥ 2. These solutions are the first known instantons, with the Chern-Pontryagin index greater than one, of the Yang-Mills model in higher dimensions. Our approach is a study of a nonlinear variational equation defined on the Poincaré half plane.