© 2022, The Author(s), under exclusive licence to The Optical Society of India.In this study, we regard the dual-mode nonlinear Schrödinger equation (DMNLSE). The DMNLSE depicts the propagations of two-moving waves synchronically. The extended rational sine–cosine and sinh–cosh methods under the homogeneous balance principle are employed for obtaining solutions. Different types of optical solitons are obtained. These solutions are new solutions for the DMNLSEs that are not reported by the other methods. The properties are displayed with figures for these solutions. Moreover, the stability analysis is also discussed. The obtained outcomes demonstrate that these structure methods are straightforward, efficient, brief and can be used in better complex phenomena with the help of symbolic computations.