3-DIMENSIONAL STEADY WATER-WAVES GENERATED BY PARTIALLY LOCALIZED PRESSURE DISTURBANCES

The author constructs a class of three-dimensional exact steady water waves resulting from a partially localized pressure disturbance on the free surface. The term partially localized means that the pressure disturbances are periodic in the direction of the flow and are decaying rapidly in the transverse direction. The resulting exact steady flows exhibit symmetric doubly periodic wave patterns at infinity on either side of the pressure disturbance. The surface tension effect is taken into account, and this enables the author to use the Implicit Function Theorem in his construction.