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Explicit Optical Dromions With Kerr Law Having Fractional Temporal Evolution

Author

Listed:
  • GANGWEI WANG

    (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, P. R. China)

  • QIN ZHOU

    (Research Group of Nonlinear Optical Science and Technology, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430200, P. R. China)

  • ALI SALEH ALSHOMRANI

    (Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • ANJAN BISWAS

    (Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA3Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia5Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Highway, Moscow 115409, Russian Federation6Department of Applied Sciences, Cross-Border Faculty, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati 800201, Romania7Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, South Africa)

Abstract

In this work, we derived the (2+1)-dimensional Schrödinger equation from the (2+1)-dimensional Klein–Gordon equation. We also obtained the fractional order form of this equation at the same time so as to discover the connection between them. For the (2+1)-dimensional Klein–Gordon equation, symmetries and conservation laws are pres ented. For different gauge constraint, from the perspective of conservation laws, the corresponding symmetries are obtained. After that, based on the fractional complex transform, soliton solutions of the time fractional (2+1)-dimensional Schrödinger equation are displayed. Some figures are showed behaviors of soliton solutions. It is important to discover the relationships between these equations and to obtain their explicit solutions. These solutions will perhaps provide a theoretical basis for the explanation of complex nonlinear phenomena. From the results of this paper, it is clear that the Lie symmetry method is a particularly important tool for dealing with differential equations.

Suggested Citation

  • Gangwei Wang & Qin Zhou & Ali Saleh Alshomrani & Anjan Biswas, 2023. "Explicit Optical Dromions With Kerr Law Having Fractional Temporal Evolution," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-11.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500561
    DOI: 10.1142/S0218348X23500561
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