Abstract
In this paper, the main motive is to mathematical explore the Kuralay equation, which find applications in various fields such as ferromagnetic materials, nonlinear optics, and optical fibers. The objective of this study is to investigate different types of soliton solutions and analyze the integrable motion of induced space curves. This article appropriates the traveling wave transformation allowing the partial differential equation to be changed into an ordinary differential equation. To establish these soliton solutions, the study employs the new auxiliary equation method. As an outcome, a numerous types of soliton solutions like, Periodic pattern with anti-peaked crests and anti-troughs, singular solution, mixed complex solitary shock solution, mixed singular solution, mixed shock singular solution, mixed trigonometric solution, mixed periodic, periodic solution and mixed hyperbolic solution obtain via Mathematica. In order to visualize the graphical propagation of the obtained soliton solutions, 3D, 2D, and contour graphics are generated by choosing appropriate parametric values. The impact of parameter w is also graphically displayed on the propagation of solitons.
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