N-soliton solutions for an integrable differential-difference equation with computer symbolic computation

摘要

In this paper, an integrable differential-difference equation is investigated based on its Lax representation. N-fold Darboux transformation (DT) are constructed with the aid of computer symbolic computation. As applications of N-fold DT, N-soliton solutions in terms of determinants are given. Also, soliton elastic interaction behavior of those solutions are shown graphically, which might be helpful for understanding physical phenomena.