Abstract
This article presents a survey on the exact and numerical solutions of the nonlinear long–short wave interaction system. The system performs an optical domain, which does not alter during multiplication according to a ticklish equipoise between nonlinear and linear influences in elastic surrounding (the medium that can alter the figure due to the existence of a deforming strength and comes back to its original shape in the absence of this force). The wave in this medium is obtained by vibrations that are the outcomes of the acoustic power. The modified auxiliary equation and the quintic B-spline approaches are investigated in our model to obtain a bundle of solutions to discuss new physical behaviors for this model. Moreover, the stability property is discussed for the analytical solutions via the properties related to the Hamiltonian system to show the range of the ability of solutions to be used in the applications of the model. These novel properties are explained by different types of figures. Finally, the convergence and the absolute error between the obtained solutions are discussed in a table.
Highlights
The optical treatise is scrutinized as one of the most notable studies in this era according to its different applications in many fields
The stability property is discussed for the analytical solutions via the properties related to the Hamiltonian system to show the range of the ability of solutions to be used in the applications of the model
The stability property is discussed for the obtained analytical solutions by using the Hamiltonian system
Summary
The optical treatise is scrutinized as one of the most notable studies in this era according to its different applications in many fields. Mathematicians have been deriving many approaches to create different classes of solutions that are used to clarify many physical interpretations of the optical soliton waves. This kind of waves comprises of a special type of optical field, which does not alter through multiplication.. The optical soliton is divided into two types as follows: 1. Spatial solitons: The nonlinear influence can balance the diffraction. The electromagnetic field will adjust the medium’s refractive index while it propagates, creating an architecture identical to a graded index fiber.
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