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<p>In this paper, we explore the soliton solutions and nonlinear dynamics of a physically meaningful reverse-spacetime nonlocal NLS equation by introducing a novel reduction method instead of the traditional RH approach. The reverse-spacetime nonlocal NLS equation, arising as a reverse-spacetime nonlocal reduction of the Manakov system, is physically significant since it can describe the solutions of the Manakov system with a particular initial condition. Firstly, it is shown that the traditional RH approach is difficult to be applied to study the spectral structure of the reverse-spacetime nonlocal NLS equation. Then, instead of using the traditional RH approach, we propose a novel reduction method to investigate the spectral structure of the reverse-spacetime nonlocal NLS equation. Specifically, starting from the RH formulation of the Manakov system, we explore in detail the constraints of the scattering data which are the keys to characterize the spectral structure of the reverse-spacetime nonlocal NLS equation. Then, based on the obtained spectral structure, the soliton solutions are obtained for the reverse-spacetime nonlocal NLS equation. Secondly, we perform asymptotic analysis to theoretically reveal the nonlinear soliton dynamics underlying the obtained soliton solutions. Particularly, we calculate the explicit forms of the single-soliton solutions of the reverse-spacetime nonlocal NLS equation, which are hyperbolic secant function waves. Moreover, the two-soliton interactions corresponding to two zeros of the RH problem possessing different real parts are shown to be elastic by analyzing their asymptotic states. However, corresponding to two zeros of the RH problem possessing the same real parts, the breather soliton behaviors formulated as two-soliton bound states will occur. Furthermore, the three-soliton solutions and the general <i>N</i>-soliton solutions of the reverse-spacetime nonlocal NLS equation are also calculated by solving the corresponding scattering data constraints. Thirdly, to illustrate the nonlinear soliton dynamics, we graphically demonstrate the soliton solutions via choosing suitable spectral parameters by highlighting the roles that the zeros of the RH problem play.</p>

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Soliton solutions and nonlinear dynamics of a reverse-spacetime nonlocal NLS equation via a novel reduction method

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Jianping Wu

摘要

In this paper, we explore the soliton solutions and nonlinear dynamics of a physically meaningful reverse-spacetime nonlocal NLS equation by introducing a novel reduction method instead of the traditional RH approach. The reverse-spacetime nonlocal NLS equation, arising as a reverse-spacetime nonlocal reduction of the Manakov system, is physically significant since it can describe the solutions of the Manakov system with a particular initial condition. Firstly, it is shown that the traditional RH approach is difficult to be applied to study the spectral structure of the reverse-spacetime nonlocal NLS equation. Then, instead of using the traditional RH approach, we propose a novel reduction method to investigate the spectral structure of the reverse-spacetime nonlocal NLS equation. Specifically, starting from the RH formulation of the Manakov system, we explore in detail the constraints of the scattering data which are the keys to characterize the spectral structure of the reverse-spacetime nonlocal NLS equation. Then, based on the obtained spectral structure, the soliton solutions are obtained for the reverse-spacetime nonlocal NLS equation. Secondly, we perform asymptotic analysis to theoretically reveal the nonlinear soliton dynamics underlying the obtained soliton solutions. Particularly, we calculate the explicit forms of the single-soliton solutions of the reverse-spacetime nonlocal NLS equation, which are hyperbolic secant function waves. Moreover, the two-soliton interactions corresponding to two zeros of the RH problem possessing different real parts are shown to be elastic by analyzing their asymptotic states. However, corresponding to two zeros of the RH problem possessing the same real parts, the breather soliton behaviors formulated as two-soliton bound states will occur. Furthermore, the three-soliton solutions and the general N-soliton solutions of the reverse-spacetime nonlocal NLS equation are also calculated by solving the corresponding scattering data constraints. Thirdly, to illustrate the nonlinear soliton dynamics, we graphically demonstrate the soliton solutions via choosing suitable spectral parameters by highlighting the roles that the zeros of the RH problem play.