“…The first and second terms are the linear temporal evolution term and group velocity dispersion (GVD), while third term introduces the anti-cubic nonlinear term, fourth and fifth terms account for the parabolic law nonlinearity, and sixth, seventh and eighth terms represent the IMD, SS and *Correspondence: manafianheris@tabrizu.ac.ir 2 Department of Mathematics, Ilkhchi Branch, Islamic Azad University, Ilkhchi, Iran Full list of author information is available at the end of the article ND respectively. Finally, the last three terms with θ k for k = 1, 2, 3 appear in the context of metamaterials [3,4]. The study of solitons in optical metameterials is trending as a hotspot in the field of optical materials.…”