WICK-TYPE STOCHASTIC FRACTIONAL SOLITONS SUPPORTED BY QUADRATIC-CUBIC NONLINEARITY

Chao-Qing Dai, Gangzhou Wu, Hui-Jun Li () and Yue-Yue Wang ()
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Chao-Qing Dai: College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, Lin’an, Zhejiang 311300, P. R. China
Gangzhou Wu: College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, Lin’an, Zhejiang 311300, P. R. China
Hui-Jun Li: ��Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China
Yue-Yue Wang: College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, Lin’an, Zhejiang 311300, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 07, 1-11

Abstract: When a random environment with the Gaussian white noise function is considered, the Wick-type stochastic fractional quadratic-cubic nonlinear Schrödinger equation is used to govern the propagation of optical pulse in polarization-preserving fibers. Using a new strategy, namely combining the variable-coefficient fractional Riccati equation method with the fractional derivative, Mittag–Leffler function and Hermite transformation, some special fractional solutions with the Brownian motion function including fractional bright and dark solitons, and fractional combined soliton solutions are given. Under the influence of the stochastic effect from the stochastic Brownian motion function portrayed by using the Lorentz chaotic system, some wave packets randomly appear during the propagation, and thus make fractional bright soliton travel wriggled in the both periodic dispersion system and the exponential dispersion decreasing system. However, the stochastic Brownian motion function has a more significant impact on the propagation of fractional bright soliton in the periodic dispersion system than that in the exponential dispersion decreasing system.

Keywords: Wick-Type Stochastic Fractional Soliton; Fractional Derivative; Quadratic-Cubic Nonlinearity; Brownian Motion Function; Pattern (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21501929

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