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用ｆＫｄＶ模式方程对单层二维表面波进行直接的数值研究。计算得出，在共振区域先锋孤立子的生成与Ｔ、Ｙ．Ｗｕ（吴耀祖）及Ｓ．Ｊ．Ｌｅｅ等人的结果相同。在共振点与超临界转向点之间，对每一个Ｆｒ数存在初始不稳定的单峰孤立子，其振幅随时间增加。当Ｆｒ数接近共振区时，初始孤立子分裂成先峰孤立子，即先峰孤立子生成是占优的。当Ｆｒ接近超临界转向点时，这类初始不稳定孤立子最终破碎。当Ｆｒ超过超临界转向点时，存在一类稳定的超临界孤立子，其振幅不随时间变化，但是它得自时间相关方程。这类孤立子位于驱动力上方，它的振幅随Ｆｒ的增加而减少．由于它不同于自由ＫｄＶ孤立子，因此本文称之为超临界驻定孤立子。
A direct numerical study of a single-layer two-dimensional surface wave using the fKdV mode equation. Calculated in the resonance region avant-garde soliton generation and T, Y. Wu (吴耀祖) and S. J. Lee et al. Have the same result. Between the resonance point and the supercritical steering point, there exists an initially unstable unimodal soliton for each Fr number, the amplitude of which increases with time. When the Fr number is close to the resonance region, the initial soliton splits into the first peak soliton, that is, the first peak soliton generation is dominant. When Fr approaches the supercritical turning point, such initial unstable solitons eventually break. When Fr exceeds the supercritical steering point, there exists a class of stable supercritical solitons whose amplitudes do not change with time but which are derived from the time-dependent equation. Such solitons are located above the driving force, and its amplitude decreases as Fr increases. Since it is different from the free KdV soliton, we call it a supercritical resident soliton.