Abstract
In this work, two novel integrable extensions to the Vakhnenko-Parkes equation (eVPE), namely, extended eVPE1 and eVPE2 as well as extended modified VPE1 (emVPE1) and VPE2 (emVPE2) are introduced and analyzed. In a like manner, we establish another two integrable extensions to the modified Vakhnenko-Parkes (eMVP) equations. We justify that every new extension of the newly developed equations are complete integrability using Painlev ' e test (PT). We examine the dispersion relations and the necessary condition for the existence of multiple soliton solutions (MSSs) to this family of the Vakhnenko-Parkes equation. We employ the simplified Hirota's method (HM) for solving this family and deriving the MSSs.