\begin{document}$\mathcal{PT}$\end{document}-symmetric nonlocal nonlinear Schrödinger equation are constructed by employing the Kadomtsev-Petviashvili hierarchy reduction method. The analytical expressions for rogue wave solutions of any Nth-order are given through Schur polynomials. We first analyze the dynamics of the first-order rogue waves, and find that the maximum amplitude of the rogue waves can reach any height larger than three times of the constant background amplitude. The effects of the space-shifted factor \begin{document}$x_0$\end{document} of the \begin{document}$\mathcal{PT}$\end{document}-symmetric nonlocal nonlinear Schrödinger equation in the first-order rogue wave solutions are studied, which only changes the center positions of the rogue waves. The dynamical behaviours and patterns of the second-order rogue waves are also analytically investigated. Then the relationships between Nth-order rogue wave patterns and the parameters in the analytical expressions of the rogue wave solutions are given, and the several different patterns of the higher-order rogue waves are further shown."> General higher-order rogue waves in the space-shifted <inline-formula><tex-math id="M2">\begin{document}$\mathcal{PT}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222298_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222298_M2.png"/></alternatives></inline-formula>-symmetric nonlocal nonlinear Schrödinger equation - 必威体育下载

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General higher-order rogue waves in the space-shifted $\mathcal{PT}$ -symmetric nonlocal nonlinear Schrödinger equation

Rao Ji-Guang, Chen Sheng-An, Wu Zhao-Jun, He Jin-Song
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  • Abstract views:2726
  • PDF Downloads:119
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Publishing process
  • Received Date:02 December 2022
  • Accepted Date:25 December 2022
  • Available Online:23 February 2023
  • Published Online:20 May 2023

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