General rogue waves in the Davey–Stewartson (DS)II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background in a line profile and then retreat back to the constant background again. It is also shown that multi-rogue waves describe the intera...

Hydroelastic solitary waves propagating on the surface of a three-dimensional ideal fluid through deformation an elastic sheet are studied. The problem is investigated based Benney-Luke-type equation derived via explicit non-local formulation classic water wave problem. normal form analysis carried out for newly developed equation, which results in Benney-Roskes-Davey-Stewartson (BRDS) system g...