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Soliton propagation in ultrashort fiber optics: Analytical and numerical investigation of the Fokas-Lenells equation
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DOI：10.1142/S0217984926500697.png)
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Abstract
En 中文
The nonlinear Schr & ouml;dinger equation and its generalizations are fundamental in soliton theory and nonlinear wave dynamics of optical systems. This paper deals with the integrable Fokas-Lenells (FL) equation, which describes the nonlinear propagation of ultrashort optical pulses in optical fibers. We obtain precise optical soliton solutions to the FL equation with the help of an extended Riccati equation mapping technique and an undetermined coefficients (UCs) method, with a systematic scheme for obtaining analytical solutions under some parameter conditions. To ensure accuracy and reliability in the analytical solutions, the differential transform method is utilized to find numerical solutions for comparison purposes. Physical aspects and behavior of the soliton solutions are also represented by visualizing two-dimensional, three-dimensional, and density plots of the impact of various parameters on the profiles of waves. The research illustrates a number of new families of traveling wave solutions, such as dark, bright, and combinations of dark and bright solitons, presenting useful insights on nonlinear wave propagation, interaction among solitons, and possibilities of their implementation in optical communications and photonic technologies. The originality of this paper is in the combination of an extended Riccati equation mapping method and the method of UCs to obtain novel exact soliton solutions of the FL equation, tested by numerical comparison and thorough visualization. This research not only enhances the theoretical basis of the FL equation but also provides new avenues for future work in nonlinear optics and mathematical physics.
Keywords:
Optical solitons
generalized Riccati equation mapping method (GREMM)
nonlinear Schr & ouml
dinger equation (NLSE)
undetermined coefficients (UC) method
differential transform method (DTM)
numerical simulation
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2.2
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207
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6.6K
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