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

• 作者: Chaonan Duan Fajun Yu
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: NONLOCAL NONLINEAR Schr?dinger EQUATION N-Fold DARBOUX Transformation Lax Pairs Exact Solution
• 年，卷（期）: 2018,（4）
• 页码范围: 888-900
• 页数: 13页
• 分类号: O1

摘要

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.