SOLITARY WAVES OF THE VARIANT BOUSSINESQ–BURGERS EQUATION IN A FRACTAL-DIMENSIONAL SPACE

Pin-Xia Wu (), Qian Yang and Ji-Huan He
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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

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-10

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.

Keywords: The Variant Boussinesq–Burgers Equation; He’s Fractal Derivatives; Fractal Variational Principle; Fractal Weierstrass Theorem; Solitary Waves (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500566

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DOI: 10.1142/S0218348X22500566

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