More General Soliton Solution for Vectorial Bose-Einstein Condensate

TL;DR

This paper derives more general exact soliton solutions for the coupled Gross-Pitaevskii equations describing vectorial Bose-Einstein condensates, using analytical and Darboux transformation methods to explore diverse soliton pairs.

Contribution

It introduces a novel approach to obtain broader soliton solutions for vector BECs, expanding the solution space beyond previous limitations.

Findings

Derived exact stationary solutions using analytical methods.

Constructed general soliton solutions via Darboux transformation.

Showcased various soliton pair configurations by parameter manipulation.

Abstract

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.