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Exact Traveling Wave Solutions Of The Coupled Local Fractional Nonlinear Schrã–Dinger Equations For Optical Solitons On Cantor Sets

Author

Listed:
  • LEI FU

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China)

  • YUAN-HONG BI

    (��School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot, P. R. China)

  • JING-JING LI

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China)

  • HONG-WEI YANG

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China)

Abstract

Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling wave solutions of the non-differentiable type defined on the Cantor sets are obtained. The characteristics of the particular solutions of fixed fractal dimension are discussed. It is proved that the local fractional coupled nonlinear Schrödinger equations can describe the interaction of fractal waves in optical fiber transmission.

Suggested Citation

  • Lei Fu & Yuan-Hong Bi & Jing-Jing Li & Hong-Wei Yang, 2024. "Exact Traveling Wave Solutions Of The Coupled Local Fractional Nonlinear Schrã–Dinger Equations For Optical Solitons On Cantor Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x23401187
    DOI: 10.1142/S0218348X23401187
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