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.