Abstract
The Schamel-Korteweg-de Vries (S-KdV) model is used to predict the influence of surface for deep water in the presence of solitary waves. The aim of the study is to study the governing model analytically by employing the extended modified auxiliary equation mapping approach and the extended FAN sub-equation method. The 3D, 2D and contour plots are drawn to demonstrate the physical nature of the nonlinear model for a set of parameters. As a result, dark solitons, light solitons, solitary waves, periodic solitary waves, rational functions, and elliptic function solutions are established. Furthermore, the the developed results are verified with the aid of latest computing tool such as Mathematica or Maple. The applied strategy appears to be a more powerful and efficient scheme for achieving exact solutions to a number of diversified contemporary models of recent eras.