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Bifurcation and traveling wave solution to fractional Biswas-Arshed equation with the beta time derivative

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  • Li, Zhao

Abstract

The main purpose of this paper is to study the dynamical behavior, optical soliton solution and traveling wave solution for the fractional Biswas-Arshed equation with the beta time derivative by using theory of planar dynamical system. Firstly, by employing the traveling wave transformation and other integral transformations, the fractional Biswas-Arshed equation with the beta time derivative is simplified into two-dimensional planar dynamic system. Secondly, phase portraits for the fractional Biswas-Arshed equation with the beta time derivative are plotted. Finally, based on Professor Li's three-step method, optical soliton solution and traveling wave solution of the fractional Biswas-Arshed equation with the beta time derivative are constructed, the obtained solutions give the propagation of optical solitons in nonlinear optics.

Suggested Citation

  • Li, Zhao, 2022. "Bifurcation and traveling wave solution to fractional Biswas-Arshed equation with the beta time derivative," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004593
    DOI: 10.1016/j.chaos.2022.112249
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    References listed on IDEAS

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    1. Aljoudi, Shorog, 2021. "Exact solutions of the fractional Sharma-Tasso-Olver equation and the fractional Bogoyavlenskii’s breaking soliton equations," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    2. Kucche, Kishor D. & Sutar, Sagar T., 2021. "Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Ali, Karmina K. & Faridi, Waqas Ali & Tarla, Sibel, 2024. "Phase trajectories and Chaos theory for dynamical demonstration and explicit propagating wave formation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Han, Tianyong & Li, Zhao & Shi, Kaibo & Wu, Guo-Cheng, 2022. "Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Han, Tianyong & Li, Zhao & Li, Chenyu, 2023. "Bifurcation analysis, stationary optical solitons and exact solutions for generalized nonlinear Schrödinger equation with nonlinear chromatic dispersion and quintuple power-law of refractive index in ," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    4. Li, Zhao & Huang, Chun, 2023. "Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas–Lenells model in optical fibers," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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