Affiliation:
1. College of Science China University of Petroleum Beijing China
2. School of Mathematics and Physics North China Electric Power University Beijing China
Abstract
AbstractFor the discrete PT‐symmetric nonlinear Schrödinger (dPTNLS) equation, this paper gives a rigorous proof of the N‐fold Darboux transformation (DT) and especially verifies the PT‐symmetric relation between transformed potentials in the Lax pair. Meanwhile, some determinant identities are developed in completing the proof. When the tanh‐function solution is directly selected as a seed for the focusing case, the onefold DT yields a three‐soliton solution that exhibits the solitonic behavior with a wide range of parameter regimes. Moreover, it is shown that the solution contains three pairs of asymptotic solitons, and that each asymptotic soliton can display both the dark and antidark soliton profiles or vanish as . It indicates that the focusing dPTNLS equation admits a rich variety of soliton interactions over the nonzero background, behaving like those in the continuous counterpart.
Funder
National Natural Science Foundation of China