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Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations

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  • Ma, Wen-Xiu

Abstract

The aim of this paper is to study vector nonlocal reverse-time NLS (nonlinear Schrödinger) equations and present a binary Darboux transformation by utilizing two sets of eigenfunctions and adjoint eigenfunctions. A product of N single binary Darboux transformations is explored for the resultant binary Darboux transformation. A class of soliton solutions is generated by an application starting from the zero seed potential.

Suggested Citation

  • Ma, Wen-Xiu, 2024. "Binary Darboux transformation of vector nonlocal reverse-time integrable NLS equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000900
    DOI: 10.1016/j.chaos.2024.114539
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    References listed on IDEAS

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    1. Ma, Wen-Xiu, 2021. "Binary Darboux transformation for general matrix mKdV equations and reduced counterparts," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Wang, Meng & Tian, Bo & Zhou, Tian-Yu, 2021. "Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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    Cited by:

    1. Gu, Yongyi & Peng, Liudi & Huang, Zhishang & Lai, Yongkang, 2024. "Soliton, breather, lump, interaction solutions and chaotic behavior for the (2+1)-dimensional KPSKR equation," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    2. Ma, Wen-Xiu, 2024. "An extended AKNS eigenvalue problem and its affiliated integrable Hamiltonian hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    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. Rao, Jiguang & Mihalache, Dumitru & Zhou, Fang & He, Jingsong & Chen, Sheng-An, 2024. "Dark and antidark solitons on continuous and doubly periodic backgrounds in the space-shifted nonlocal nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    5. Zhu, Yan & Li, Kehua & Huang, Chuyu & Xu, Yuanze & Zhong, Junjiang & Li, Junjie, 2025. "Abundant exact solutions of the fractional (3+1)-dimensional Yu–Toda–Sasa–Fukuyama (YTSF) Equation using the Bell Polynomial-based neural network method," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    6. Cui, Xiao-Qi & Wen, Xiao-Yong & Li, Zai-Dong, 2024. "Magnetization reversal phenomenon of higher-order lump and mixed interaction structures on periodic background in the (2+1)-dimensional Heisenberg ferromagnet spin equation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    7. Shah, Syed Asif Ali & Hussain, Ejaz & Ma, Wen-Xiu & Li, Zhao & Ragab, Adham E. & Khalaf, Tamer M., 2024. "Qualitative analysis and new variety of solitons profiles for the (1+1)-dimensional modified equal width equation," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    8. 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).
    9. Jhangeer, Adil & Beenish,, 2024. "Ferroelectric frontiers: Navigating phase portraits, chaos, multistability and sensitivity in thin-film dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    10. Ma, Wen-Xiu, 2025. "A soliton hierarchy derived from a fourth-order matrix spectral problem possessing four fields," Chaos, Solitons & Fractals, Elsevier, vol. 195(C).
    11. Liu, Shao-Hua & Tian, Bo & Gao, Xiao-Tian, 2024. "Generalized (n,N−n)-fold Darboux transformation and localized waves for an integrable reduced spin Hirota-Maxwell-Bloch system in an erbium doped fiber," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).

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