Formulas for the asymptotics of some class of integrals of rapidly oscillating functions that generalize the well-known stationary phase method, which were obtained in the previous paper of the author, are applied to integrals arising in the well-known tsunami hydrodynamic piston model in the case of a constant pool bottom. As a result, asymptotic formulas are obtained for the head part of the wave for large values of the time elapsed since the occurrence of the tsunami. These formulas contain some special reference integrals and have different forms depending on combinations of wave and time parameters.

中文翻译：

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广义平稳相位法在流体动力活塞模型海啸头波渐近中的应用

作者的先前论文中得出的，归纳了众所周知的固定相法的一类快速振荡函数的积分的渐近公式，应用于著名的海啸水力活塞模型中的积分。池底恒定的情况。结果，对于自海啸发生以来所经过的时间的较大值，获得了波的头部的渐近公式。这些公式包含一些特殊的参考积分，并且根据波动和时间参数的组合具有不同的形式。