Exact Soliton Dynamics and Stability Analysis of a Fractional Order Coupled Wu-Zhang System via a Generalized Riccati−Bernoulli−Bäcklund Approach

To investigate the fractional coupled Wu-Zhang system analytically, this paper uses a hybrid generalized Riccati−Bernoulli sub-ODE scheme and Bäcklund transformation to find the exact kink, antikink, and bright-kink soliton solutions. The dynamical properties of these solutions are discussed using Hamiltonian formulation, phase-portrait analysis, and maximum Lyapunov exponent calculation, including the observation of a change between stable and unstable regimes. The effect of the fractional-order parameter α on waveform morphology, dispersion, and stability are graphically visualized in 2D and 3D. These findings illustrate that the proposed method is effective in the measurement of various soliton structures, and it offers a strong paradigm for examining nonlinear fractional wave dynamics, which has been used in soliton theory, long-wave propagation, optical pulses, and nonlinear fluid and plasma interactions.