N-SOLITON, BREATHER, LUMP SOLUTIONS AND DIVERSE TRAVELING WAVE SOLUTIONS OF THE FRACTIONAL (2 + 1)-DIMENSIONAL BOUSSINESQ EQUATION

Kang-Jia Wang, Jing-Hua Liu, Jing Si, Feng Shi and Guo-Dong Wang
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Kang-Jia Wang: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Jing-Hua Liu: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Jing Si: School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China
Feng Shi: 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

FRACTALS (fractals), 2023, vol. 31, issue 03, 1-15

Abstract: The (2 + 1)-dimensional Boussinesq equation plays a key role in modeling the shallow water. In this work, we derive a new fractional (2 + 1)-dimensional Boussinesq equation based on the conformable fractional derivative for the first time. By means of the Hirota bilinear method, we obtain the N-soliton, breather and lump solutions. In addition, the abundant traveling wave solutions like bright solitary, dark solitary wave solutions are investigated by applying the variational method. The solutions are presented through the 3D plots and 2D contours by assigning the proper parameters. The corresponding physical interpretations are also elaborated. The findings in this work are expected to open some new horizons on the study of fractional PDEs in physics.

Keywords: Conformable Fractional Derivative; Hirota Bilinear Method; Variational Method; Semi-Inverse Method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500238

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