More General Soliton Solution for Vectorial Bose-Einstein Condensate

WE derive exact and more general solutions of the two coupled Gross-Pitaevskii equation with suitable parameters by demonstrating two analytical methods. In the first method, equations are analysed and inferred some of their mathematical and physical properties, which are then used to derive the exact stationary solutions. In the second method, we demonstrate the Darboux transformation method and construct exact and more general soliton solutions for the Gross-Pitaevskii equation (NLS equation with external potential term). We have proved that the solutions were more general one by showcasing all kinds of soliton pairs by manoeuvring the parameters suitably.