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In this article, the q-deformed Sinh–Gordon equation has been investigated using exp(−ϕ(ξ))-expansion and the generalized projective Riccati equations (GPRE) methods. These methods successfully extract trigonometric and hyperbolic solutions along with the suitable constraint conditions, imposed on parameters for the existence of solutions. Besides that, the numerical results are displayed through various graphics to show the diverse propagation patterns of solitons. The proposed equation has opened new horizons for modeling those physical system where symmetry is violated.