Manipulating localized matter waves in multi-component Bose-Einstein condensates

TL;DR

This paper explores how localized matter waves in two- and three-component Bose-Einstein condensates can be manipulated using variable trap potentials, revealing diverse rogue wave and soliton solutions through similarity transformation techniques.

Contribution

It introduces a method to generate and analyze localized wave solutions in multi-component BECs with variable nonlinearity and trap potentials, including new rogue wave configurations.

Findings

Existence of rogue waves, solitons, and breathers in different trap potentials.

Deformation of density profiles with trap parameter tuning.

Construction of multi-rogue wave solutions for multi-component BECs.

Abstract

We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameter and external trap potential through similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schr\"{o}dinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures, namely rogue waves, dark-and bright soliton-rogue wave, and rogue wave-breather-like wave for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Further we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single, two and three composite rogue waves for three component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.