DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS

摘要

In this paper,we study a differential-difference equation associated with discrete 3 × 3 matrix spectral problem.Based on gauge transformation of the spectral problm,Darboux transformation of the differential-difference equation is given.In order to solve the differential-difference equation,a systematic algebraic algorithm is given.As an application,explicit soliton solutions of the differential-difference equation are given.