Abstract
In the current study, we investigate the dynamicity of soliton propagation of the Schrödinger–Hirota (SH) equation amidst the presence of third-order dispersion by employing the Riccati equation method and extended tanh expansion method. These approaches revealed quite new exact optical soliton solutions that generalized the recently constructed solitons in the literature. The constraint conditions guaranteeing the validation of these solitons are also determined. Also, to shed more light on the characteristics and features of these solitons, we give some graphical illustrations using the three-dimensional representations.