A NEW PERSPECTIVE ON THE STUDY OF THE FRACTAL COUPLED BOUSSINESQ–BURGER EQUATION IN SHALLOW WATER

Kang-Jia Wang, Guo-Dong Wang and Hong-Wei Zhu
Additional contact information
Kang-Jia Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Guo-Dong Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Hong-Wei Zhu: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-13

Abstract: The well-known coupled Boussinesq–Burger equation can be used to describe the flow of the shallow water of the harbor. But when the boundary is nonsmooth, it becomes powerless. So, the fractal calculus is needed to be applied to it and the fractal coupled Boussinesq–Burger equation (FCBBe) is presented for the first time in this paper. By using the semiinverse method, we have successfully established the fractal variational formulation of the FCBBe, which can not only provide the conservation laws in an energy form in the fractal space but also reveal the possible solution structures of the equation. Then a novel variational approach based on He’s variational method and the two-scale transform are used to seek its periodic wave solutions. The main advantage of variational approach is that it can reduce the order of differential equation and make the equation more simple. Finally, the numerical results have been shown through graphs to discuss the effect of different fractal orders on the wave motion. The obtained results in this work are expected to shed a bright light on the study of fractal nonlinear partial differential equations in the fractal space.

Keywords: Fractal Variational Principle; Periodic Wave Solution; Semiinverse Method; He’s Variational Method; Fractal Coupled Boussinesq–Burger Equation (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X2150122X
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x2150122x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X2150122X

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().