Finding the Necessary Conditions for the Existence of the Dark Soliton Solution to the Vakhnenko-Parkes Equation with Variable Coefficients and with Power Law Nonlinearity

This research aims to find the necessary conditions for the existence of the dark soliton solution to the Vakhnenko-Parkes equation with time dependent coefficients and with power law nonlinearity by using the solitary wave ansatz method. The value of the power law nonlinearity parameter is determined. The results show that the used method is efficient to obtain this kind of solutions for the nonlinear partial differential equations.