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Solitary Waves Of The Variant Boussinesq–Burgers Equation In A Fractal-Dimensional Space

Author

Listed:
  • PIN-XIA WU

    (School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P. R. China)

  • QIAN YANG

    (�School of Science, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, P. R. China)

  • JI-HUAN HE

    (��School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454003, P. R. China‡National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, Jiangsu 215123, P. R. China§School of Science, Xi’an University of Architecture and Technology, Xi’an, Shaanxi 710055, P. R. China)

Abstract

In this work, we mainly focus on the fractal variant Boussinesq–Burgers equation which can well describe the motion of shallow water traveling along an unsmooth boundary. First, we construct its fractal variational principle and prove its strong minimum condition by the fractal Weierstrass theorem. Then two types of soliton solutions are acquired according to the constructed fractal variational principle. We find that the order of the fractal derivative hardly affects the whole shape of the solitary waves, but it remarkably affects its propagation process.

Suggested Citation

  • Pin-Xia Wu & Qian Yang & Ji-Huan He, 2022. "Solitary Waves Of The Variant Boussinesq–Burgers Equation In A Fractal-Dimensional Space," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-10, May.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500566
    DOI: 10.1142/S0218348X22500566
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