Optimizing space curve motion in Kuralay model through diverse soliton approaches

This paper delves into an investigation of the Kuralay model, with a particular emphasis on the Kuralay-II system. The primary objective of this research is to analyze the integrable motion of space curves generated by these equations. The proposed equation can be classified as a type of nonlinear Schrödinger equation, generates integrable long short waves models and enhances our knowledge of optical soliton dynamics in different physical systems. The novelty of this research lies in the utilization of three distinct methodologies, namely the unified solver method, \(exp(-\chi (\eta ))\) $exp(-\chi (\eta ))$ approach, and ansatz methods, for extracting optical soliton solutions to these equations. These solutions take the form of dark, bright, singular, and periodic optical solitons. In order to provide an understanding of these optical soliton solutions, we present 3D, 2D, and density plots to elucidate the physical characteristics. Furthermore, we provide a comparative analysis of the employed techniques. The outcomes obtained may also prove beneficial for shaping future modeling endeavors. The techniques employed in this study have demonstrated their effectiveness, and reliability in addressing additional non-linear partial differential equations.