Solitonic fusion and fission for a (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

Water waves are observed in, e.g., the rivers, lakes or oceans. In this Letter, the investigation is conducted on a (3 + 1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves. Based on the Hirota method and symbolic computation, we obtain some X-type, Y-type and periodic lump-stripe soliton solutions. For the X-type soliton solutions, we observe the fusion and fission phenomena. For the Y-type soliton solutions, combined with the asymptotic analysis, we observe the fission phenomenon. For the periodic lump-stripe soliton solutions, we observe the fusion phenomenon between the periodic lump and stripe soliton. Periodic lump disappears and is finally swallowed by the stripe soliton during the propagation, which implies that the interaction is inelastic. Furthermore, we analyse the influences of the coefficients of the equation on the periodic lump-stripe soliton solutions. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This study investigates a (3 + 1)-dimensional generalized nonlinear evolution equation in shallow water waves and obtains X-type, Y-type, and periodic lump-stripe soliton solutions through symbolic computation and the Hirota method. Fusion and fission phenomena are observed in the X-type soliton solutions, while the fission phenomenon is observed in the Y-type soliton solutions. The interaction between periodic lump and stripe solitons is found to be inelastic.