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Inverse scattering transform for the coupled Lakshmanan–Porsezian–Daniel equations with non-zero boundary conditions in optical fiber communications

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  • Han, Peng-Fei
  • Ye, Ru-Suo
  • Zhang, Yi

Abstract

The challenge of solving the initial value problem for the coupled Lakshmanan–Porsezian–Daniel equations which involves non-zero boundary conditions at infinity is addressed by the development of a suitable inverse scattering transform. Analytical properties of the Jost eigenfunctions are examined, along with the analysis of scattering coefficient characteristics. This analysis not only leads to the derivation of additional auxiliary eigenfunctions but also is necessary for a comprehensive investigation of the fundamental eigenfunctions. Two symmetry conditions are discussed for studying the eigenfunctions and scattering coefficients. These symmetry results are utilized to rigorously define the discrete spectrum and ascertain the corresponding symmetries of scattering datas. The inverse scattering problem is formulated by the Riemann–Hilbert problem. Subsequently, we derive analytical solutions from the coupled Lakshmanan–Porsezian–Daniel equations with a detailed examination of the novel soliton solutions.

Suggested Citation

  • Han, Peng-Fei & Ye, Ru-Suo & Zhang, Yi, 2025. "Inverse scattering transform for the coupled Lakshmanan–Porsezian–Daniel equations with non-zero boundary conditions in optical fiber communications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 483-503.
    • Handle: RePEc:eee:matcom:v:232:y:2025:i:c:p:483-503
    DOI: 10.1016/j.matcom.2025.01.008
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    References listed on IDEAS

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    1. Liu, Meng-Meng, 2023. "M-lump solutions to the (2+1)-dimensional generalized Calogero–Bogoyavlenshii–Schiff equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 118-129.
    2. Wu, Zhi-Jia & Tian, Shou-Fu, 2023. "Breather-to-soliton conversions and their mechanisms of the (2+1)-dimensional generalized Hirota–Satsuma–Ito equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 235-259.
    3. Han, Peng-Fei & Zhang, Yi, 2024. "Investigation of shallow water waves near the coast or in lake environments via the KdV–Calogero–Bogoyavlenskii–Schiff equation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Pinar Izgi, Zehra, 2023. "Rogue waves and solitons of the generalized modified nonlinear Schrödinger equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 535-549.
    5. Li, Yan & Hao, Xiazhi & Yao, Ruoxia & Xia, Yarong & Shen, Yali, 2023. "Nonlinear superposition among lump soliton, stripe solitons and other nonlinear localized waves of the (2+1)-dimensional cpKP-BKP equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 57-70.
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    1. Dumitru Vieru & Constantin Fetecau, 2025. "Influence of Magnetic Field and Porous Medium on Taylor–Couette Flows of Second Grade Fluids Due to Time-Dependent Couples on a Circular Cylinder," Mathematics, MDPI, vol. 13(13), pages 1-20, July.

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