Computational simulations; propagation behavior of the Riemann wave interacting with the long wave

Abstract

The analytical solutions to the (2+1)-dimensional integrable Schwarz-Korteweg-de Vries (SKdV) problem are investigated in this article. To get solitary wave formulae such as complex, exponential, hyperbolic, and trigonometric function solutions, the modified Khater technique and the improved Bernoulli sub-equation function method (IBSEFM) are used. Furthermore, their stability characteristics are investigated. The solutions produced using the two methods are compared in order to uncover relationships between them and their features as indicated by the appropriate parameter values.