Optical Soliton Solution of the Benney–Roskes/Zakharov–Rubenchik Systems

Abstract

The study focuses on deriving optical soliton solutions for the Benney–Roskes (BR) and Zakharov–Rubenchik (ZR) system. To achieve this, complex wave transformations are applied to convert the system of partial differential equations (PDEs) into a more manageable form of ordinary differential equation (ODE). This transformation simplifies the analysis and facilitates the extraction of exact solutions. The new Kudryashov method (nKM) is employed to solve the resulting nonlinear ODE (NODE). This powerful analytical technique allows for the derivation of various types of soliton solutions, including bright solitons, kink solitons, and singular solitons. Each type of soliton represents different physical phenomena and wave behaviors, providing a comprehensive understanding of the system’s dynamics. The study includes the visualization of the obtained soliton solutions through graphical representations. These visualizations help in understanding the spatial and temporal evolution of the solitons and their interaction with the medium. Furthermore, the study analyzes how changes in the system’s parameters individually affect the shape, amplitude, and width of the solitons. This parametric analysis is crucial for predicting and controlling soliton behavior in practical applications. These are the main distinctive parts and novelties of this study. By deriving and analyzing soliton solutions, the study provides deeper insights into the nonlinear interactions within the BR and ZR system. Understanding these interactions is essential for applications in optical communications, where solitons can be used to transmit information over long distances without significant loss or distortion.