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

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 Schrödinger 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.

18 pages, Accepted for publication in Phys. Rev. E

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• Spontaneous generation of dark-bright and dark-antidark solitons upon quenching a particle-imbalanced bosonic mixture
• Rogue waves on an elliptic function background in complex modified Korteweg-de Vries equation
• An analysis of spatiotemporal localized solutions in the variable coefficients (3+1)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters
• Vector rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling
• Analytical solutions of the coupled Gross-Pitaevskii equations for the three-species Bose-Einstein condensates
• Provable bounds for the Korteweg-de Vries reduction in multi-component Nonlinear Schrodinger Equation