This study investigates the Wu-Zhang system, a nonlinear dispersive wave equation having applications in nonlinear optics, plasma physics, and material science that is crucial for modeling shallow water wave dynamics. The Riccati-Bernoulli sub-equation method and the Kumar-Malik approach are two advanced and contemporary methods used to study the behavior of the Wu-Zhang system. These approaches offer a wide range of soliton solutions including exponential, periodic, trigonometric, hyperbolic, and Jacobi elliptic solutions which have diverse applications in the field of fluid dynamics, nonlinear quantum optics, nonlinear Acoustics, and plasma physics. At first, a traveling wave transformation is applied to reduce the Wu-Zhang system into an ordinary differential equation(ODE). We used the Riccati-Bernoulli sub-equation approach in conjunction with the Kumar-Malik approach to solve the resulting ordinary differential equation. Next, we create a two-dimensional dynamical system from our ODE. Additionally, a Hamiltonian structure is created to examine energy interaction, soliton structure robustness, and conservation law sustainability. A thorough analysis of sensitivity is carried out in order to examine the effects of changes in initial conditions and running parameters on the dynamical pattern of solitons. This study serves as a significant development in the domain of nonlinear wave theory by broadening the analytical framework and uncovering the overlooked areas in existing documents. For insight of dynamical patterns of solutions, 3-dimensional, 2-dimensional, contour, and density plots are generated with the help of Wolfram Mathematica software.
Amjad et al. (Wed,) studied this question.