Propagation of nonlinear dispersive waves in shallow water and acoustic media in the framework of integrable Schwarz–Korteweg–de Vries equation

This article investigated the solitary wave solutions to the (2+1)-dimensional integrable Schwarz–Korteweg–de Vries equation. The proposed model is particularly applicable to shallow water wave dynamics and may also extend to contexts such as acoustic wave propagation, nonlinear electric media, and oceanic wave phenomena. First, we constructed the ordinary differential equation form of the nonlinear partial differential equation with the help of the traveling wave transformation. After that, we utilized the generalized Arnous method and the modified sub-equation method to construct the solitary waves containing hyperbolic, exponential, trigonometric, and inverse functions. Using suitable parameter values, the graphical aspects of solutions are demonstrated by plotting a 3D surface plot (including a contour and density plot), a 2D surface plot, a streamline plot, and a polar plot. By utilizing these approaches, accurate analytical solutions for soliton waves were generated, which comprise kink, bright, and dark waves. We employed the generalized Arnous method and the modified sub-equation method to formulate a technique for addressing integrable systems, providing a valuable framework for examining nonlinear phenomena across various physical contexts. This study's outcomes enhance both nonlinear dynamical processes and solitary wave theory.