In the present study, by implementing the direct algebraic method, we present the traveling wave solutions for some different kinds of the Korteweg–de Vries (KdV) equations. The exact solutions of the Kawahara, fifth order KdV and generalized fifth order KdV equations are obtained. Solutions for the Kawahara, fifth order KdV and generalized fifth order KdV equations are obtained precisely and efficiency of the method can be demonstrated. The stability of these solutions and the movement role of the waves by making the graphs of the exact solutions are analyzed. All solutions are exact and stable, and have applications in physics.
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Seadawy et al. (2016) studied this question.
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