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The aim of this paper is to investigate the integrable motion of induced curves using the Kuralay equation, which is a complex integrable coupled system. The soliton solutions derived from Kuralay equation are supposed to represent the most advanced research in several significant phenomena, including optical fibers, nonlinear optics, and ferromagnetic materials. Analytical methods are used to obtain traveling wave solutions for this model as the Cauchy problem cannot be addressed by the inverse scattering transform. In order to find the solitary wave solutions, the new extended direct algebraic and Nucci's reduction approaches are taken over. As a result, the new extended direct algebraic method provides singular, mixed singular, periodic, mixed trigonometric, complex combo, trigonometric, mixed hyperbolic, plane, and combined bright-dark soliton solutions. The Nucci's reduction technique develops the first integral of differential equation to discuss the conservation and exact solutions. To ensure the sensitivity of the study, the effect of waves on the propagation of solitons and the sensitivity of the model is examined. To illustrate how the fitting values of the system parameters may be utilized to anticipate the behavioral reactions to pulse propagation, the resulting solutions are visually shown in 2D and 3D charts.
Faridi et al. (Tue,) studied this question.