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In this paper, the nonlinear fractional Kairat-X equation is investigated on the basis of computational simulation. The nonlinear fractional Kairat-X equation is an integrable equation and is used to explain the differential geometry of curves and equivalence aspects. Several kinds of solitary wave structures of the nonlinear fractional Kairat-X equation are established successfully via the implantation of the extended simple equation method. Here, we explore the interesting, novel and general solutions in trigonometric, exponential, and rational types, which represent periodic wave solitons, mixed solitons in the shape of bright–dark solutions, kink wave solitons, peakon bright and dark solitons, anti-kink wave solutions, bright solitons, dark solitons, and solitary wave structure. The physical structures of secured results, aided by numerical simulation, have numerous applications in applied sciences such as optical fiber, geophysics, laser optics, mathematical physics, nonlinear optics, nonlinear dynamics, communication system, and engineering. This study explores the physical behavior of models through the visualization of solutions in contour, 2D and 3D plots by revealing that these solutions yield profitable results in the field of mathematical physics. The study demonstrates that the proposed technique is more reliable, efficient, and powerful in analyzing nonlinear evolution equations in various domains of science. [ABSTRACT FROM AUTHOR]

In this paper, we successfully extracted the various types of soliton solutions for the complex nonlinear Kuralay-II equation through the improved F-expansion method with symbolic computational software Mathematica. The extracted soliton solutions for the Kuralay-II equation are interesting, novel and more general such as anti-kink wave solitons, dark solitons, kink wave solitons, bright solitons, periodic wave solitons, mixed solitons in bright-dark soliton shape, peakon solitons, and solitary wave structures. The graphical structure of some extracted solutions is visualized in 2D, 3D and contour plottings with imaginary, real, and absolute values of the functions by using the numerical simulation. The proposed research will contribute to advancing our knowledge about the complex nonlinear Kuralay-II equation and demonstrating the applicability to the proposed approach to investigate other higher-order complex nonlinear equations. The successful investigation demonstrated that the proposed method is effective, simple, more powerful, efficient and can be utilized on a variety of other nonlinear equations. The explored solitary waves and optical solitons will play an important role in the investigation of nonlinear phenomena in various domains of science and engineering. [ABSTRACT FROM AUTHOR]