New solutions for the generalized q-deformed sinh-Gordon equation with q-calculus

Our objective in this paper is to investigate the sinh-Gordon equation’s generalization using a q-calculus. This equation explains systems with broken symmetries. The q-deformed sinh-Gordon equation adds noncommutativity and non-linearity, expanding on its original form. We compare two methods for solving this equation: RqDTM and VIM. RqDTM is a modified differential transform technique for q-deformed equations, whereas VIM utilizes an iterative approach. We give numerical results and compare the accuracy and efficiency of the solutions achieved using these approaches. This analysis evaluates the merits and disadvantages of each strategy for solving the q-deformed sinh-Gordon equation, offering insights into their applicability and performance. •Generalized q-Deformed Sinh-Gordon equation.•Reduced q-differential transform method (RqDTM).•Variational iteration method (VIM).•New analytical and numerical solutions.