Yu, F. and Feng, S. (2017) Explicit Solution and Darboux Transformation for a New Discrete Integrable Soliton Hierarchy with 4 × 4 Lax Pairs. Mathematical Methods in the Applied Sciences, 40, 5515-5525.
https://doi.org/10.1002/mma.4406

has been cited by the following article:

• TITLE: N-Fold Darboux Transformation for the Nonlocal Nonlinear Schrödinger (NNLS) Equation with the Self-Induced PT-Symmetric Potential

  AUTHORS: Chaonan Duan, Fajun Yu

  KEYWORDS: Nonlocal Nonlinear Schrödinger Equation, N-Fold Darboux Transformation, Lax Pairs, Exact Solution

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.4, April 27, 2018

  ABSTRACT: The Darboux transformation (DT) method is studied in a lot of local equations, but there are few of work to solve nonlocal equations by DT. In this letter, we solve the nonlocal nonlinear Schrödinger equation (NNLSE) with the self-induced PT-symmetric potential by DT. Then the N-fold DT of NNLSE is derived with the help of the gauge transformation between the Lax pairs. Then we derive some novel exact solutions including the bright soliton, breather wave soliton. In particularly, the dynamic features of one-soliton, two-soliton, three-soliton solutions and the elastic interactions between the two solitons are displayed.