A Higher-Dimensional Lie Algebra and 4×4 Discrete Soliton Hierarchy with Self-Consistent Sources

Abstract

In this paper, we aim to construct a super integrable discrete soliton hierarchy with self-consistent sources. A new isospectral problem is firstly presented, and we consider a discrete soliton hierarchy with self-consistent sources by using Lie algebra . Then, a new higher dimensional super integrable discrete soliton hierarchy with self-consistent sources is obtained. The method can be generalized to other soliton hierarchy with self-consistent sources.