Analytical and numerical study for the generalized q-deformed sinh-Gordon equation

Abstract In this article, we study the generalized q q -deformed sinh-Gordon equation analytically using the new general form of Kudryashov’s approach and numerically using the finite difference method. We develop a general form of the Kudryashov method that contains more than one constant that is used to give more explanations for the solutions that are obtained. The numerical results are also presented using the finite difference approach. We also provide numerous figures to demonstrate the various solitons propagation patterns. The proposed equation has opened up new options for describing physical systems that have lost their symmetry. The equation under study has not been studied extensively, so we completed the lesson that started a short time ago on it.