Novel soliton wave solutions of the Vakhnenko–Parkes equation arising in the relaxation medium

This study checks the solitary wave solutions of the nonlinear Vakhnenko–Parkes (VP) equation that was derived by Parkes in 1998 to describe the high-frequency waves’ dynamical and physical behavior in the relaxation medium. The solitary wave solutions of the nonlinear VP model are computationally investigated by implementing the Khater II method. Many soliton solutions are constructed and represented in some distinct graphs. The stability property of these solutions is also investigated. All obtained solutions’ accuracy is checked by putting them back into the original model by employing Mathematica 12. The method's performance shows its effectiveness, power, and ability to handle some nonlinear evolution equations.