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This paper pays attention to secure the different forms of optical soliton solutions to the spinor Bose–Einstein condensate. Three-component Gross–Pitaevskii (tc-GP) system which describes the F = 1 spinor Bose–Einstein condensate (BEC), with F denoting the atom’s spin, is used as a governing model to secure the solutions in BEC. Superfluidity and superconductivity are two properties of the low-temperature phenomenon that are associated with the BEC, which is formed by a diluted atomic gas. There has been an increasing interest in studying multi-component equations because they can be utilized to explain a wide range of complicated physical phenomena and have more dynamical structures of localized wave solutions. New extended direct algebraic method (NEDAM), a recently developed integration tool, is used to secure the solution. Different kinds of solitons, such as dark, singular, kink, bright–dark, complex and combined, are extracted. In addition, hyperbolic, exponential type and periodic solutions are guaranteed. Nonlinear partial differential equations (NLPDEs) are well-explained by the technique since it offers previously derived solutions and also extracts new exact solutions by incorporating the results of multiple procedures. In addition to discussing the physical representation of some solutions, we also plot 3D, 2D and contour graphs using the appropriate parameter values. The findings of this paper can improve the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the methodology used. We believe that a large number of engineering model specialists will benefit from this research. Findings suggest that the algorithm employed is efficient, prompt, succinct and applicable to complex systems.
Younas et al. (Thu,) studied this question.