In this paper, we apply the extended Kudryashov method to construct some new exact solitary wave solutions of three important physical models, Schamel-nonlinear Schrödinger (S-NLS) equation, Schamel Korteweg-de Vries (S-KdV) equation, Schamel Korteweg-de Vries Burgers (S-KdVB) equation. In addition, this method is applied to seek solutions of Schamel equation modeling ion-acoustic waves in plasma and dust plasma. With the aid of symbolic computation, explicit exact solutions of these equations are expressed in terms of the hyperbolic functions, the trigonometric functions, and the exponential function. The stability of some exact solutions is computationally studied.