Extraction of new optical solitons and MI analysis to three coupled Gross–Pitaevskii system in the spinor Bose–Einstein condensate

Abstract

This article investigates the optical solitons to the three coupled Gross–Pitaevskii (GP) system (also called the non-linear Schrödinger (NLS) equation), which describes the [Formula: see text] spinor Bose–Einstein condensate, with [Formula: see text] denoting the atom’s spin. The solutions are expressed in the form of hyperbolic function solutions that have different physical meanings such that the hyperbolic tangent appears in the calculation and rapidity of special relativity while, the hyperbolic cotangent arises in the Langevin function for magnetic polarization, the hyperbolic secant arises in the profile of a laminar jet. The various kinds of soliton solutions in single and combined form like bright, dark, singular as well as bright-dark and singular in the mixed form are also extracted by the mean of extended sinh-Gordon equation expansion method. By using the appropriate values of the involved parameters, 3D, 2D and their corresponding contour graphs are sketched for physical movement of the attained results. We also discuss the modulation instability (MI) analysis of the governing model. The constraint conditions for the existence of soliton solutions are also mentioned. The calculated work and earned results show the power, effectiveness, and the simplicity of applied method to discuss the soliton solutions as the contrast with other analytical schemes. The main outcome of the proposed technique is that we have succeeded in a single move to get and organize various types of new solutions.