General soliton solutions to a \(\varvec{(2+1)}\)-dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

Original Paper
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Abstract

We investigate a \((2+1)\)-dimensional nonlocal nonlinear Schrödinger equation with the self-induced parity-time symmetric potential. By employing the Hirota’s bilinear method and the KP hierarchy reduction method, general soliton solutions to the \((2+1)\)-dimensional nonlocal NLS equation with zero and nonzero boundary conditions are derived. These solutions are given in forms of Gram-type determinants. We first construct general bright solitons with zero boundary condition by constraining the tau functions of two-component KP hierarchy. Furthermore, we derive general dark and antidark solitons with nonzero boundary from the tau functions of single-component KP hierarchy.

Keywords

\((2+1)\)-Dimensional nonlocal nonlinear Schrödinger Soliton solution Hirota’s bilinear method KP hierarchy reduction method 

Notes

Acknowledgements

The author thanks Prof. Jingsong He of Ningbo university for many discussions and suggestions on the paper. This work is supported by the Doctoral Scientific Research Foundation of Shandong Technology and Business University under Grant No. BS201703.

Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interests.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematic and Information ScienceShandong Technology and Business UniversityYantaiPeople’s Republic of China

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