Eur. Phys. J. Plus (2021) 136: 925
https://doi.org/10.1140/epjp/s13360-021-01925-8

Regular Article

Dynamic analysis of hybrid solutions for the new (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation with time-dependent coefficients in incompressible fluid

College of Mathematics Science, Inner Mongolia Normal University, 010022, Huhhot, People’s Republic of China

^a 448024030@qq.com
^b tgts@imnu.edu.cn

Received: 5 May 2021
Accepted: 31 August 2021
Published online: 9 September 2021

Abstract

Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In this work, the new (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation with time-dependent coefficients in incompressible fluid is investigated via the Hirota bilinear method. To this end, by considering the Hirota bilinear form of the equation and utilizing the homoclinic test method along with symbolic computations, an existence theorem and corollary about hybrid solutions of this equation are proved. Furthermore, the mixed high-order lump N-soliton solutions and the hybrid solutions are obtained analytically, and the novel evolutionary behaviors are shown by 3D figures. Additionally, a comparison has been given with some recent papers to show that our results are novel.