Traveling wave solutions, numerical solutions, and stability analysis of the (2+1) conformal time-fractional generalized q-deformed sinh-Gordon equation

The two-dimensional conformal time-fractional generalized -deformed sinh-Gordon equation has been used to model a variety of physical systems, including soliton propagation in asymmetric media, nonlinear waves in optical fibers, quantum field theory, and condensed matter physics. The equation is able to capture the complex dynamics of these systems and has been shown to be a powerful tool for studying them. This article discusses the two-dimensional conformal time-fractional generalized -deformed sinh-Gordon equation both analytically and numerically using Kudryashov’s approach and the finite difference method. In addition, the stability analysis and local truncation error of the equation are discussed. A number of illustrations are also included to show the various solitons propagation patterns. The proposed equation has opened up new possibilities for modeling asymmetric physical systems.