Diverse Soliton Structures of Induced Curves in the Integrable Coupled Kuralay Equation

This study explores the integrable coupled Kuralay equation, which is widely utilized to study the motion of induced curves. In fields such as ferromagnetic materials, nonlinear optics, and optical fibers, soliton solutions of the Kuralay equation have emerged as significant recent developments. For proposed model, diverse soliton structures are obtained analytically by using two techniques, the unified method and the sub-ordinary differential equation (ODE) approach. It is possible to extract soliton solutions for rational and polynomial functions with a unified technique. Proposed research uses the new sub-ODE method to provide accurate solutions for soliton waves, such as hyperbolic, periodic, dark, bright, trigonometric, Jacobi elliptic, and Weierstrass elliptic function solutions. Moreover, sensitivity analysis of proposed model is successfully analyzed by using different initial condition. The physical relevance of the proposed model by referring to the visual representation of the achieved soliton solutions. The derived solutions are presented in 2D, 3D, and contour plots to illustrate how system parameters influence pulse propagation behavior.