Solitons propagation in magneto-optic waveguides having generalized anti-cubic law of nonlinearity

In this paper, we explore new optical solitons for the coupled nonlinear Schrödinger equation with generalized anti-cubic nonlinearity, which governs the propagation of electromagnetic waves in magneto-optic waveguides. These components play a crucial role in optical transmission lines and lasers, being utilized in integrated optical circuits as modulators, circulators, and isolators. To retrieve optical soliton solutions, we have implemented, for the first time, two powerful schemes for the model equation, namely the modified Sardar sub-equation method and the new Φ⁶-model expansion method. As a result, we obtained a wide variety of new soliton solutions, including bright, dark, gray, dark bell-type, kink, anti-kink, singular, mixed bright-singular, and dark-singular solitons. Additionally, various other solution forms emerged, such as Jacobi elliptic functions, periodic, and rational solutions. Finally, by extracting parametric conditions for the existence of soliton solutions, we discovered that physical parameters, including inter-modal dispersions, self-steepening effect, nonlinear dispersion, and the magneto-optic effect, play a crucial role in both the existence and shaping of the extracted solitons.