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Elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger equations
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  • Bo-wen Li,
  • Tao Xu,
  • Tian-Li Zhang,
  • Li-cong An,
  • Yang Chen
Bo-wen Li
China University of Petroleum Beijing

Corresponding Author:[email protected]

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Tao Xu
China University of Petroleum Beijing
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Tian-Li Zhang
China University of Petroleum Beijing
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Li-cong An
China University of Petroleum Beijing
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Yang Chen
China University of Petroleum Beijing
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Abstract

In this paper, we obtain the stationary elliptic- and hyperbolic-function solutions of the nonlocal reverse-time and reverse-space-time nonlinear Schrödinger (NLS) equations based on their connection with the standard Weierstrass elliptic equation. The reverse-time NLS equation possesses the bounded dn-, cn-, sn-, sech-, and tanh-function solutions. Of special interest, the tanh-function solution can display both the dark- and antidark-soliton profiles. The reverse-space-time NLS equation admits the general Jacobian elliptic-function solutions (which are exponentially growing at one infinity or display the periodical oscillation in x), the bounded dn- and cn-function solutions, as well as the K-shifted dn- and sn-function solutions. At the degeneration, the hyperbolic-function solutions may exhibit an exponential growth behavior at one infinity, or show the gray- and bright-soliton profiles.
20 Aug 2021Submitted to Mathematical Methods in the Applied Sciences
23 Aug 2021Submission Checks Completed
23 Aug 2021Assigned to Editor
13 Sep 2021Reviewer(s) Assigned
17 Apr 2022Review(s) Completed, Editorial Evaluation Pending
12 May 2022Editorial Decision: Accept
30 Nov 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 17 on pages 10877-10890. 10.1002/mma.8422