New structural dynamics of isolated waves via the coupled nonlinear Maccari’s system with complex structure

In this study, the modified exp (-ϕ(η))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\phi (\eta ))$$\end{document}-expansion function method is utilized in acquiring some new results to the coupled nonlinear Maccari’s system. The Maccari’s system is a nonlinear model that describes the dynamics of isolated waves, confined in a small part of space, in various fields such as hydrodynamic, plasma physics and nonlinear optics. We construct some new results with a complex structure to this model, such as; the trigonometric and hyperbolic function solutions. Under the suitable choice of the values of parameters, we plot the 2D, 3D and the contour graphs to some of the obtained solutions in this study. We observed that our results may be helpful in detecting the movement of an isolated wave in a small space to some practical physical problems.