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
Accepted: 31 December 2020
Published online: 13 January 2021
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 . 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.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021