This paper retrieves quiescent optical solitons that merge from magneto-optic waveguides that maintain Kudryashov’s form of self–phase modulation coupled with a generalized form of non–local nonlinearity. The model also comes with nonlinear chromatic dispersion and is considered with generalized temporal evolution. The enhanced direct algebraic method has made this retrieval possible. A full spectrum of solitons is thus recovered through the intermediary Jacobi’s elliptic functions as well as Weierstrass’ elliptic functions. The parameter constraints for the existence of such solitons are also enumerated.