Exact solitons of an \(N\)-component discrete coupled integrable system

Abstract— An \(N\)-component discrete coupled (dC) system is presented. The Lax pair of the system is written in terms of \(2\times 2\) matrices and generalized to \(2^N\times 2^N\) matrices, giving rise to an \(N\)-component discrete coupled system. A Darboux matrix is introduced to construct solutions of the Lax pair equations giving rise to solutions of the dC system. Soliton solutions of the dC system are computed and their interactions are studied.