Nonlinear Dynamics

, Volume 96, Issue 3, pp 2103–2114 | Cite as

A nonlocal nonlinear Schrödinger equation derived from a two-layer fluid model

  • Xi-zhong LiuEmail author
  • Jun Yu
Original Paper


By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then, a general form of nonlocal nonlinear Schrödinger (NNLS) equation with shifted parity, charge conjugate and delayed time reversal is obtained by using multi-scale expansion method. Some kinds of elliptic periodic wave solutions of the NNLS equation, which become soliton solutions and kink solutions when the modulus is taken as unity, are obtained by using elliptic function expansion method. Some representative figures of these solutions are given and analyzed in detail. In addition, by carrying out the classical symmetry method on the NNLS equation, not only the Lie symmetry group but also the related symmetry reduction solutions are given.


Nonlocal nonlinear Schrödinger equation Periodic waves Symmetry reduction solutions 



The authors are grateful to the referee, whose comments and suggestions of the earlier version of the paper have led to a substantial clarification and revision of work. This work was supported by the National Natural Science Foundation of China under Grant Nos. 11405110, 11275129 and the Natural Science Foundation of Zhejiang Province of China under Grant No. LY18A050001.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest to this work.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute of Nonlinear ScienceShaoxing UniversityShaoxingChina

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