Bidirectional wave dynamics with a variety of physical structures to the q-Deformed Sinh-Gordon model: a graphical exploration

This manuscript introduces a novel bidirectional wave dynamics to the q-deformed Sinh-Gordon model. The main objective of this study is to investigate the simultaneous motion of two symmetrical waves. The ϕ6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^{6}$$\end{document}-model expansion technique is used for achieving the required objective. The ϕ6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ^{6}$$\end{document}-model expansion technique extracts new solitary wave solutions for the proposed model. Moreover, we delve into the mathematical aspects and explore the physical characteristics of the q-deformed Sinh-Gordon equation in its bidirectional form. The study provides intricate derivations of the innovative solutions, accompanied by visual representations that offer insights into their physical structures. The findings of this investigation significantly contribute to our comprehension of this model. Finally, fascinating three-dimensional plots and two-dimensional line plots are displayed.