This current research explores a new generalized q-deformed \(\sinh \) -Gordon equation. The governing equation is frequently used to model plasma-based solutions, complex optical science, photonic transmission systems, ultrashort burst lasers to identify objects and other theoretical sciences. The work consists of two goals. Firstly, analytically using the modified extended \(\tanh \) function approach. Precise results for the derived equation are obtained that could be used to simulate physical systems with broken symmetries and to consider events involving amplification or dissipation. Secondly, with the help of a numerical approach investigate the error function between the q-demormed terms. Several figures have been included to illustrate the different optical solitons propagation patterns.
