Spatial wave dynamics of steady oblique wave interactions

In several models for waves on water of finite depth, a great variety of su rface-elevation profiles for steadily traveling waves can be generated by a spatial evolution law in which the time-like variable is one of the horizo ntal space variables. This is the case for both linear and weakly nonlinear models, including the Kadomtsev-Petviashvili equation (KP-II); Al the line ar level, these waves correspond to steady oblique interactions of one-dime nsional wave trains. The shape of the waves is determined in a similar way in all cases - by initial data that specifies the wave slope along a single line oriented either parallel or perpendicular to the direction of propaga tion. As one application we compute a steady two-dimensional wake due to a pressure disturbance moving at near-critical speed in a weakly nonlinear re gime. We find that the disturbance can generate solitary waves traveling ob liquely in the wake, a phenomenon recently realized experimentally and foun d to be relevant to the safe operation of high-speed ferries. (C) 2000 Else vier Science B.V. All rights reserved.