Nonlinear wave-group interaction during the long time evolution of wave trains

The long time evolution of wave trains exhibits distinct wave-group shapes across different nonlinear stages. To further investigate the characteristics of nonlinear wave-group interaction during this prolonged evolution, the High-Order Spectral method and wavelet transform analysis are employed, and a novel spatial wave-group identification method suitable for long time evolution is introduced. The wave groups in the evolution process are classified into four types based on their length. It reveals that in the stage of modulation instability, all wave groups belong to Type I, resulting from modulation instability. They propagate at the same velocity without energy exchange, maintaining independent evolution. The emergence of the other three types of wave groups indicates the existence of nonlinear wave-group interaction. As nonlinear wave-group interaction becomes dominant, the characteristic parameters and velocities of wave groups undergo significant changes. Moreover, when two wave groups with different velocities merge, the resulting group accelerates instead of slowing down. Subsequently, the participating wave groups separate once again, with the originally trailing wave group overtakes the originally leading one, and their velocities eventually converge. Notably, different types of wave groups are both results of nonlinear interactions and fundamental units in subsequent interaction process.