Eur. Phys. J. Plus (2021) 136: 77
https://doi.org/10.1140/epjp/s13360-020-01062-8

Regular Article

Novel resonant multi-soliton solutions and inelastic interactions to the (3 + 1)- and (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equations via the simplified linear superposition principle

Department of Aeronautics and Astronautics, Air Force Academy, 820, Kaohsiung, Taiwan, ROC

^a afckkuo@gmail.com, lon12110213@yahoo.com.tw

Received: 25 May 2020
Accepted: 31 December 2020
Published online: 13 January 2021

Abstract

In this paper, the resonant solitary waves to the (3 + 1)- and (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equations are exposed via the simplified linear superposition principle (LSP). Based on the related Hirota’s bilinear equations, the resonant multi-soliton solutions and the corresponding wave numbers are formally generated. Abundant inelastic interactions, i.e., fission and fusion of traveling N-solitary waves, are presented analytically and graphically. Besides, we show that the velocity resonance (VR) is not applicable to handle the (3 + 1)- and (4 + 1)-dimensional BLMP equations, due to that the dispersion relation is constructed as $\omega =-k^3$. The results show that the simplified LSP provides enough freedom to construct resonant multi-soliton waves that has potential applications to a large variety of real physical phenomena.