Nonlinear Modulation of Stationary Water Waves

抄録

This paper deals with the far field modulation of stationary capillary-gravity waves produced by an obstacle on a fluid layer of uniform depth moving with a uniform speed. By using the derivative expansion method it is found that, to the lowest order of approximation, the complex amplitude of the surface elevation is kept constant along a particular direction which will be called ‘group direction’ and, to the next order of approximation, it is governed by the nonlinear Schrödinger equation. The known properties of this equation suggest that, in the far field from the wave source, there may exist spatial envelope solitons, cavitons and phase jumps depending upon the group directions.