Applications of soliton solutions of the two-dimensional nonlinear complex coupled Maccari equations

Abstract

<p>This study investigates the two-dimensional nonlinear complex coupled Maccari equations, which are significant in describing solitary waves concentrated in small spatial regions. These equations have applications across various fields, including hydrodynamics, nonlinear optics, and the study of sonic Langmuir solitons. Using the Bäcklund transformation, we explore a broad range of soliton solutions for this system, focusing on their spectral properties. The proposed method stands out for its simplicity and comprehensive results compared to traditional approaches. The obtained solutions are expressed in rigorous, trigonometric, and hyperbolic forms, providing deeper insights into the dynamics of the system. To enhance understanding, we present contour and three-dimensional graphical representations of the solutions. This study has potential applications in energy and industry by advancing the understanding of nonlinear wave phenomena, which are crucial in optimizing energy transfer processes and designing efficient systems in hydrodynamic and optical engineering. Additionally, the soliton solutions obtained here contribute to technologies in power transmission and high-speed optical communications, offering a foundation for innovations in sustainable energy systems and industrial applications.</p>