Eur. Phys. J. Plus (2020) 135: 167
https://doi.org/10.1140/epjp/s13360-020-00109-0

Regular Article

M-lump, interaction between lumps and stripe solitons solutions to the (2+1)-dimensional KP-BBM equation

¹ Department of Applied Mathematics, Faculty of Mathematical Science, University of Tabriz, Tabriz, Iran
² Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq
³ Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
⁴ Department of Mechanical Engineering, College of Engineering, University of Zakho, Zakho, Iraq
⁵ Department of Mechanical Engineering, Urmia University, Urmia, Iran

^* e-mail: j_manafianheris@tabrizu.ac.ir

Received: 14 October 2019
Accepted: 3 January 2020
Published online: 28 January 2020

Abstract

In this paper, we have earned the M-lump solutions, the interaction within stripe solitons and lumps which are more considered mentioning that lumps will be drowned or swallowed by the stripe solitons. By utilizing the Hirota bilinear method and via the symbolic calculations, solve the ()-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. We obtain some multiple collisions of lumps. Next, the interactive solutions between M-lumps and N-stripe solitons have very enhanced the existing literature on the KP-BBM equation. Through the three-dimensional plots, contour, and two-dimensional plots by utilizing Maple software, the physical properties of these waves are described very well. That will be extensively used to describe many interesting physical phenomena in the areas of gas, plasma, optics, acoustics, heat transfer, fluid dynamics, classical mechanics, and so on. These new results can help us better understand interesting physical phenomena and mechanisms.