EXACT TRAVELING WAVE SOLUTIONS OF THE COUPLED LOCAL FRACTIONAL NONLINEAR SCHRÖDINGER EQUATIONS FOR OPTICAL SOLITONS ON CANTOR SETS

Lei Fu, Yuan-Hong Bi, Jing-Jing Li and Hong-Wei Yang
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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

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-10

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.

Keywords: Exact Traveling Wave Solution; Coupled Local Fractional Nonlinear Schrödinger Equation; Optical Soliton; Fractals (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401187

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