Reduced matrix integrable hierarchies via group reduction involving off-diagonal block matrices

Abstract

Abstract This paper proposes an innovative form of group reduction or similarity transformation involving off-diagonal block matrices. The proposed method is applied to the Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problem, leading to the generation of reduced matrix AKNS integrable hierarchies. As a result, a variety of reduced multiple-component integrable nonlinear Schrödinger and modified Korteweg–de Vries models are derived from the analysis of the reduced AKNS matrix spectral problem.