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This paper investigates a recently introduced (2 + 1) -dimensional extended Calogero–Bogoyavlenskii–Schiff equation. The considered model is widely used in fluid dynamics, nonlinear optics and plasma physics. The study of the governing equation has provided insights into the dynamical behaviors of wave systems, which is an important area of research in applied mathematics and theoretical physics. Firstly, the description of the generalized Kudryashov and the two variable ( G ′ G , 1 G) -expansion methods is presented. The governing model is converted into a nonlinear ordinary differential equation by utilizing the traveling wave hypothesis. A family of exact traveling wave solutions such as solitons and solitary waves are extracted using the two proposed methods for the governing model. The graphical demonstrations are presented to examine the physical behavior of the constructed solutions. Kink solitary wave, singular kink, W-shape soliton, dark-bright soliton and periodic wave solutions are successfully retrieved. The proposed techniques are utilized to examine the governing model for the first time in this work to the best of our knowledge. The acquired results will help in guiding future investigations of the wave phenomena represented by the considered equation. [ABSTRACT FROM AUTHOR]

The (2+1)-dimensional extended Calogero–Bogoyavlenskii–Schiff equation appears in the mathematical description of physical phenomena in plasma physics, fluid dynamics and nonlinear optics. In this article, extended trial and modified auxiliary equation methods are utilized to observe the dynamical structures exhibiting the solitary wave behavior of the considered model. The traveling wave hypothesis is employed to extract explicit closed-form solution expressions. The presented methods show reliability and robust computational capabilities to investigate solitary waves. In order to investigate the physical behavior of these solutions, 3D, 2D and density plots are drawn for different values of parameters. The graphical observations depict kink soliton, dark–bright singular soliton and periodic wave solutions. The comparison of the outcomes of the proposed results with those obtained using prior techniques is made to confirm the usefulness of the proposed techniques. The presented study will be helpful to explain the wave propagation in many problems of plasma physics and fluid dynamics. Moreover, the reported solutions may help to understand optical wave transmission and aid in the development of optical devices. The results given in this study will contribute in the understanding of the behavior of waves in the higher-dimensional governing models. [ABSTRACT FROM AUTHOR]