Soliton solutions of a (3+1)-dimensional nonlinear evolution equation for modeling the dynamics of ocean waves

The (3+1)-dimensional generalized nonlinear evolution equation (gNLEE) is analyzed to model oceanic waves. One-parameter Lie group of infinitesimal transformations method is applied to the (3+1)-dimensional gNLEE. Invariant condition satisfying fourth-order prolongation and generators of infinitesimal transformations are found. The (3+1)-dimensional gNLEE is reduced to ordinary differential equations (ODEs) for the different vector fields obtained by the Lie group of transformations method. The key finding for the study of breathers and solitons that account for waveform perturbation and dispersion, including nonlinear impacts, is elaborated. Discussion of wave-wave interactions, using graphic interpretation, to explain the formation of directional large-amplitude rogue waves is explained. It is found that the scale in the crest direction becomes finite as the coherence becomes diagonal. In addition, unstable wave fields, beam dynamics, and interactions among solitons are seen.