In this study, the uses of unified method for finding solutions of a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. We successfully construct solutions to these equations. For each of the derived solutions, we provide the parametric requirements for the existence of a valid soliton. In order to visualize some of the discovered solutions, we plot the 2D and 3D graphics. The results of this investigation, which have been presented, might be useful in elucidating the model's physical significance. These are a highly useful tool for studying how electrical solitons, which travel as voltage waves in nonlinear dispersive media, spread out, as well as for doing various physical calculations. The study’s findings, which have been disclosed, might be useful in illuminating the models under consideration's physical significance and electrical field.

The Oskolkov equation, which is a nonlinear model that describes the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid, is examined in the present study. It has been obtained by applying the modified ( G ′ ∕G ) -expansion method, especially using calculation results such as kink wave, cusp wave, periodic respiratory waves, and periodic wave solutions. This research has employed this process to seek novel computational results of the Oskolkov equation. The dynamics of obtained wave solutions are analyzed and illustrated in figures by selecting appropriate parameters. With three dimensional, two dimensional, and contour graphical illustration, mathematical results explicitly exhibit the proposed algorithm's complete honesty and high performance in physics, mathematics, and engineering. KEYWORDS incompressible visco-elastic Kelvin-Voigt fluid, modified (G ′ ∕G)-expansion method, Oskolkov equation, wave solutions MSC CLASSIFICATION

In this study, the uses of unified method for finding solutions of a nonlinear Schrodinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. We successfully construct solutions to these equations. For each of the derived solutions, we provide the parametric requirements for the existence of a valid soliton. In order to visualize some of the discovered solutions, we plot the 2D and 3D graphics. The results of this investigation, which have been presented, might be useful in elucidating the model's physical significance. These are a highly useful tool for studying how electrical solitons, which travel as voltage waves in nonlinear dispersive media, spread out, as well as for doing various physical calculations. The study's findings, which have been disclosed, might be useful in illuminating the models under consideration's physical significance and electrical field.

Under examination in this manuscript is a (2+1)-D generalized Calogero–Bogoyavlenskii–Schiff equation is considered through a criterion variable transition in which a dominating variable involved. Based on the Hirota bilinear method, we build novel structures entirely innovative lump solutions, periodic solutions in separable form, and periodic-soliton solutions and also perforated appearance of two-solitary wave are obtained. Furthermore, we demonstrate that the constraints that lump solutions meet are through to satisfy a number of significant features, such as navigation, polarity and nonlinear analysis. With the aid of Maple, the 3-D plot and contour plot, the physical properties of these vibrations are very effectively explained. The obtained results can improve the dynamics of higher-dimensional nonlinear water wave’s scenarios in fluids and plasma phenomena.

This paper studies to secure closed-form optical solitons moving using the optical fibers of the Biswas-Arshed model (BAM) with nonlinear Kerr law using the modified G ’ / G -expansion scheme. The obtained results current optical periodic wave shape, double periodic optical solitons, optical shock wave, the interaction between lump wave shape and periodic optical wave shape, the interaction between rough wave shape and optical soliton wave shapes for the model constructions. We display some two- and three-dimensional results from the nonlinear model under study. In communication sciences and optical fiber communications, mathematical findings plainly show the proposed algorithm’s total honesty and high performance through three-dimensional, two-dimensional, and contour graphical illustration.