Study on Nonlinear Wake Interaction

The most important feature of the wakes of fast ships in restricted waters is that solitary waves can be generated ahead of the ship. Using the Korteweg de Vries equation and the sign and auxiliary results of the Hirota bilinear form, this study derives a two-soliton solution with different phase changes. All possible waveforms of the two-soliton solution of the Kadovtsev-Petviashvili(KP) equation for different phase changes and the waveforms of the decomposition structure and linear superposition of the two-soliton solution are obtained using Mathematica. This establishes a foundation for understanding the two-soliton solution of the KP equation, two-soliton interaction, and its morphological characteristics. Based on the two-soliton solution of the dimensionless KP equation, the study simulates the surface height of the interaction region of equal and unequal amplitude incident solitons with standard coordinates. The results show that the amplitude difference between the equal amplitude incident soliton and the amplitude of the reference soliton is 0.01% larger than that of the 1% difference in the space of the interaction peak. The interaction of two incoming solitons with unequal amplitudes results in the bending of their wave humps. The different wave humps of the incoming soliton and two-soliton solution at the center of interaction area are obtained using MATLAB. Finally, the slopes of the interacting solitons are compared by adjusting the parameter k. Results show that for a higher value of k, the profile of the interacting soliton is narrower and the slope along the propagation direction of the wave crest is greater.