On optical soliton solutions of the higher-order Lakshmanan-Porsezian-Daniel model having the cubic-quintic-septic law in the presence of spatio-temporal and chromatic dispersion

The higher-order Lakshmanan-Porsezian-Daniel equation (LPDE) with the cubic-quintic-septic (CQS) law having spatiotemporal and chromatic dispersion terms (STD-CD) is examined to derive new optical soliton solutions. To accomplish this aim, we operated on a simple version of the new extended auxiliary equation method (SAEM26). The optical soliton solutions of the LPDE with CQS as well as STD-CD are constructed in detail. Moreover, 3D-surface, contour, and 2D plots are presented for the bright and periodic singular soliton solutions. Additionally, the effects of diverse model parameters on the bright soliton structure are surveyed, and these effects are displayed with 2D graphics. The findings established in this work can positively contribute to research in nonlinear optics, while the SAEM26 can be effectively applied to similar nonlinear models.