DMS-9500956 Vanden-Broeck This proposal is concerned with the study of waves propagating at the surface of a fluid. An important example is the train of waves generated by an obstacle (i.e. a ship) moving at a constant velocity at the surface of water. Existing theories are based on a number of simplifying assumptions. It is proposed to extend and improve existing theories by removing some of these assumptions. It is expected that the research will uncover new families of solutions. In particular it is proposed to study the effect of a layer of mud on ship waves. The proposed approach consists of replacing the classical assumption of a rigid bottom by an appropriate boundary condition derived from lubrication theory. It is also proposed to calculate periodic and solitary waves in presence of vorticity and surface tension. Previous and preliminary calculations have shown that there are many different families of solutions. It is intended to study them further and to calculate numerically the interaction between solitary waves.
