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A novel Riemann–Hilbert formulation-based reduction method to an integrable reverse-space nonlocal Manakov equation and its applications

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  • Wu, Jianping

Abstract

In this paper, a novel Riemann–Hilbert (RH) formulation-based reduction method is developed for an integrable reverse-space nonlocal Manakov equation. Firstly, the scattering-data constraints of the reverse-space nonlocal Manakov equation are shown to be difficult to determine via the traditional RH method. Secondly, to obtain the scattering-data constraints of the reverse-space nonlocal Manakov equation, the traditional RH method is extended to an improved version which we call a novel RH formulation-based reduction method. Specifically, utilizing the RH formulation-based reduction method, the scattering-data constraints of the reverse-space nonlocal Manakov equation are determined to guarantee the required nonlocal symmetry reduction of the two-component Ablowitz–Kaup–Newell–Segur (AKNS) system. Moreover, the scattering-data constraints of the reverse-space nonlocal Manakov equation are compared with those of the Manakov equation. Thirdly, N-soliton solutions of the reverse-space nonlocal Manakov equation are obtained by imposing the obtained scattering-data constraints in those of the two-component AKNS system. Furthermore, the applications of our novel RH formulation-based reduction method are confirmed by applying it to another integrable nonlocal Manakov equation of reverse-spacetime type. Moreover, the scattering-data constraints of the reverse-spacetime nonlocal Manakov equation are further compared with those of the reverse-space nonlocal Manakov equation and the Manakov equation, respectively. Additionally, the nonlinear soliton features of the reverse-space nonlocal Manakov equation and the reverse-spacetime nonlocal Manakov equation are analyzed and classified in detail, respectively, according to different spectral parameter selections.

Suggested Citation

  • Wu, Jianping, 2025. "A novel Riemann–Hilbert formulation-based reduction method to an integrable reverse-space nonlocal Manakov equation and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077925000104
    DOI: 10.1016/j.chaos.2025.115997
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    References listed on IDEAS

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    1. Li Cheng & Wen-Xiu Ma, 2023. "Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations," Mathematics, MDPI, vol. 11(19), pages 1-8, September.
    2. Ma, Wen-Xiu, 2024. "Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Wu, Jianping, 2024. "Spectral structures and soliton dynamical behaviors of two shifted nonlocal NLS equations via a novel Riemann–Hilbert approach: A reverse-time NLS equation and a reverse-spacetime NLS equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
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