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The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time. Generating partial differential equations and conditions of existence of the generalized KdV solitary waves are derived using the inverse balancing method. Computational experiments illustrate the variety of new solitary solutions and their generating equations.doi:10.21595/jve.2016.16941 fatcat:5w6ox3dnxvcixm7maayhls6gti