N-Fold Darboux Transformation for the Nonlocal Nonlinear Schrödinger (NNLS) Equation with the Self-Induced PT-Symmetric Potential - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.4, April 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 4 (April 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

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

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DOI: 10.4236/jamp.2018.64076 754 Downloads 1,590 Views Citations

Author(s)

Chaonan Duan, Fajun Yu^*

Affiliation(s)

School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, China.

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.

KEYWORDS

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

Share and Cite:

Duan, C. and Yu, F. (2018) N-Fold Darboux Transformation for the Nonlocal Nonlinear Schrödinger (NNLS) Equation with the Self-Induced PT-Symmetric Potential. Journal of Applied Mathematics and Physics, 6, 888-900. doi: 10.4236/jamp.2018.64076.

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[2]	N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions. Mathematics 2021, 9, 733
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[3]	N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions
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[4]	Darboux transformation and exact solutions for high order nonlocal coupled akns system
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