We have generalized the new Bogning-Djeumen Tchaho-Kofané method based on the construction of the solitary wave solutions. This method has been adopted to facilitate the resolution or the construction of certain types of nonlinear partial differential equations where the nonlinear terms and dispersive terms coexist. Transformations associated with this method have been pre-established. The method has been also extended to the theory of instability.

solitary wave, BDKm, instability, range of coefficient, hyperbolic functions.