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.

分析 (3+1) 维广义非线性演化方程 (gNLEE) 以模拟海浪。无穷小变换方法的一参数李群应用于(3+1)维gNLEE。找到了满足四阶延展的不变条件和无穷小变换的生成器。对于通过李群变换方法获得的不同矢量场，(3+1) 维 gNLEE 被简化为常微分方程 (ODE)。详细阐述了解释波形扰动和色散（包括非线性影响）的呼吸器和孤子研究的关键发现。对波-波相互作用的讨论，使用图形解释来解释定向大振幅流氓波的形成。发现随着相干性变为对角线，波峰方向的尺度变得有限。此外，还可以看到不稳定的波场、光束动力学和孤子之间的相互作用。