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The generalized Schamel-Korteweg-de Vries (S-KdV) equation containing root of degree nonlinearity is a very attractive model for the study of ion-acoustic waves in plasma and dusty plasma. In this work, we obtain the soliton-like solutions, the kink solutions, and the plural solutions of the generalized S-KdV equation by using the sine-cosine method. These solutions may be of important significance for the explanation of some practical physical problems. It is shown that these two methods provide a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.

Exact Solitary Wave Solutions for the Generalized Schamel Korteweg–De Vries Equation