Manipulating localized matter waves in multicomponent 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.

On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients

“…Motivated by this, several studies have also been undertaken to identify the localized solutions in coupled NLS equations with constant coefficients [33,34,35,36,37,38,39,40,41,42,43]. Subsequently attempts have been made to identify the localized solutions such as bright-bright, bright-dark, dark-dark soliton and RW solutions in the coupled vcNLS equations (in one-dimensions) [44,45,46,47,48,49,50,51]. Very recently attempts have been made to identify RW and breather solutions in the (2+1)-dimensional coupled vcNLS equations [52,53].…”

Formation of rogue waves on the periodic background in a fifth-order nonlinear Schrödinger equation

“…One can verify that the upper right component (J 12 ) that appear in the matrix Eq. ( 15), yields the same second-order ODE (14).…”

“…The formation of RWs can be related to the modulation instability of the wave background [8,9,10]. Based on the theoretical arguements it has been shown that RWs can arise on different backgrounds, including constant, multi-soliton and periodic backgrounds [11,12,13,14,15]. On the other hand, in nature, surface of the ocean and the waves that appear on it may exhibit periodic phenomena.…”

Rogue waves on the double-periodic background in Hirota equation

“…In nature, RWs can arise from a variety of backgrounds, including constant background, multi-soliton background and periodic wave background [24][25][26][27][28]. Recently, interest has been a e-mail: velan@cnld.bdu.ac.in (corresponding author) 0123456789().…”