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Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation

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  • dos Santos, Mateus C.P.

Abstract

In this paper, we investigate the dynamics and stability of multi-peak solitons from the coupled nonlinear Schrödinger equation with the fractional dimension based on Lévy random flights. By implementing linear stability analysis and direct simulations, we demonstrate regions where the single and multi-peak modes are stable. Analysis of perturbed coupled solitons confirms the stability of higher-order modes compared to lower-order modes under the same configurations. The stability diagrams show that the force coupling, Lévy index, power, and the nonlinear intensity significantly influence the stability of high-order modes. Our findings indicate that stability is favored in self-defocusing systems with high Lévy indices under weak coupling conditions, with higher-order states exhibiting smaller stability regions.

Suggested Citation

  • dos Santos, Mateus C.P., 2024. "Orthogonal multi-peak solitons from the coupled fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004685
    DOI: 10.1016/j.chaos.2024.114916
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    1. Jason W. Fleischer & Mordechai Segev & Nikolaos K. Efremidis & Demetrios N. Christodoulides, 2003. "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature, Nature, vol. 422(6928), pages 147-150, March.
    2. Li, S.R. & Bao, Y.Y. & Liu, Y.H. & Xu, T.F., 2022. "Bright solitons in fractional coupler with spatially periodical modulated nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Li, Pengfei & Malomed, Boris A. & Mihalache, Dumitru, 2020. "Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Lenzi, E.K. & de Castro, A.S.M. & Mendes, R.S., 2019. "Time dependent solutions for fractional coupled Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 622-632.
    5. Shilong Liu & Yingwen Zhang & Boris A. Malomed & Ebrahim Karimi, 2023. "Experimental realisations of the fractional Schrödinger equation in the temporal domain," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    6. Qiu, Yunli & Malomed, Boris A. & Mihalache, Dumitru & Zhu, Xing & Peng, Xi & He, Yingji, 2020. "Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Zeng, Liangwei & Mihalache, Dumitru & Malomed, Boris A. & Lu, Xiaowei & Cai, Yi & Zhu, Qifan & Li, Jingzhen, 2021. "Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Zeng, Liangwei & Belić, Milivoj R. & Mihalache, Dumitru & Wang, Qing & Chen, Junbo & Shi, Jincheng & Cai, Yi & Lu, Xiaowei & Li, Jingzhen, 2021. "Solitons in spin-orbit-coupled systems with fractional spatial derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    9. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
    10. Kevin E. Strecker & Guthrie B. Partridge & Andrew G. Truscott & Randall G. Hulet, 2002. "Formation and propagation of matter-wave soliton trains," Nature, Nature, vol. 417(6885), pages 150-153, May.
    11. Zeng, Liangwei & Zeng, Jianhua, 2020. "Fractional quantum couplers," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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