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

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 Schrӧdinger 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.

N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

“…Recently there has been an additional interest that has caused a hot topic of research, mainly due to Mark J. Ablowitz and Ziad H. Musslimani developed the nonlocal NLS equations [23,24]. In [25], Zhenya Yan introduced a new integrable nonlocal general vector NLS equation and found its exact solutions (See many other interesting examples about nonlocal NLS equations in [26][27][28][29] ).…”