Application of the Generalized Stationary Phase Method to the Asymptotics of the Tsunami Head Wave in the Hydrodynamic Piston Model

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.