The three-dimensional (3-D) nonlinear and dispersive PDEs system for surface waves propagating at undisturbed water surface under the gravity force and surface tension effects are studied. By applying the reductive perturbation method, we derive the (2 + 1) -dimensions form of the Davey-Stewartson (DS) system for the modulation of 2-D harmonic waves. By using the simplest equation method, we find exact traveling wave solutions and a general form of the multiple-soliton solution of the DS model. The dispersion analysis as well as the conservatio...
