VARIATIONAL PRINCIPLES FOR FRACTAL WHITHAM–BROER–KAUP EQUATIONS IN SHALLOW WATER

Kang-Jia Wang and Kang-Le Wang
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Kang-Jia Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Kang-Le Wang: ��School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 02, 1-9

Abstract: In this paper, we mainly consider the Whitham–Broer–Kaup equations with unsmooth boundaries, and a new fractal derivative is adopted to construct the fractal model. The variational principles of the fractal Whitham–Broer–Kaup equations are successfully constructed by fractal Semi-inverse method, which is helpful to study the symmetry, discover the conserved quantity, and has a wide application prospect in numerical simulation. The results are discussed by the two-scale transform method. The approximate analytical solutions of the fractal Whitham–Broer–Kaup equations are obtained according to the variational iteration method and two-scale transform method.

Keywords: Fractal Derivative; Whitham–Broer–Kaup Equation; Variational Principle; Fractal Semi-Inverse Method; Two-Scale Transform Method (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500286

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