Soliton dynamics and qualitative analysis of the (2+1)-dimensional Konopelchenko–Dubrovsky system

The Konopelchenko–Dubrovsky (KD) model, which predicts the propagation of nonlinear waves in various physical media, including fluids in elastic tubes, dusty plasmas, and highly nonlinear optical systems, is investigated in this study using a powerful analytical method known as the Jacobi elliptic function (JEF) method. Numerous accurate wave solutions, including various stable wave forms and pulse shapes and different kinds of trigonometric and hyperbolic wave forms, are produced by this method. We present graphical representations of the dynamical behavior of the governing equation using various tools like phase portraits, time series and sensitivity analysis, Poincare maps, power spectra, and analysis of the system’s energy and stability. The qualitative analysis of the system in terms of its Hamiltonian structure makes it possible to distinguish bistable double-well and stable single-well potential energy landscapes, which are shown to correspond directly to the formation of kink solitons and periodic wave solutions, respectively. This paper provides a more physical background to the bifurcations of solutions and the changeovers between various wave forms. In addition to strengthening our knowledge of nonlinear wave propagation, the study offers a flexible framework for investigating additional nonlinear evolution equations in applied scientific and engineering settings.