Approximate Simulations for the Non-linear Long-Short Wave Interaction System

This research paper studies the semi-analytical, and numerical solutions of on the nonlinear long-short wave interaction system which represents an optical field that does not alter through multiplication due to a sensitive balance between linear and nonlinear impacts in the elastic medium that is defined as the medium which can adjust in the figure as a consequence of a deforming strength and come back its shape to its original form when the force eliminates. In this medium, the wave is produced by vibrations that are a consequence of acoustic power and is known as a sound wave or acoustic wave. The Adomian decomposition method and cubic\,\&\, septic B-spline method are applied to the suggested system to obtain distinct types of solutions that are used to explain the novel physical properties of this system. These novels' features are described by different types of figures that show more physical properties of this model. Also, the convergence between the obtained solutions is discussed by some tables that show the values of absolute error between them.