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In this article, we numerically investigate the vortex nucleation in a Bose-Einstein condensate trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed the Feynmans rule for the number of vortices versus angular momentum in Bose-Einstein condensates in presence of the density dependent-gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density dependent-gauge potential., Comment: Accepted for publication in Phys. Rev. E, 10 figures, 10 pages

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, $\Omega_{\text{cr}}$, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the $\Omega_{\text{cr}}$ values for vortex nucleation. The critical frequencies and thereby, the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional $\textit{s}$-wave scattering lengths through the strength of nonlinear rotation, $\mathit{C}$, such that $\Omega_{\text{cr}}(\mathit{C}>0) < \Omega_{\text{cr}}(\mathit{C}=0) < \Omega_{\text{cr}}(\mathit{C}<0)$. In an analogous manner, the critical ellipticity ($\epsilon_{\text{cr}}$) for vortex nucleation during an adiabatic introduction of trap ellipticity ($\epsilon$) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs., Comment: 10 pages, 10 figures, Accepted for publication in PRE

By means of linear stability analysis (LSA) and direct numerical simulations of the coupled Gross-Pitaevskii(GP)equations, we address the impurity induced modulational instability (MI) and the associated nonlinear dynamics in Bose-Einstein condensates (BECs). We explore the dual role played by the impurities within the BECs -- the instigation of MI and the dissipation of the initially generated solitary waves. Because of the impurities, the repulsive BECs are even modulationally unstable and this tendency towards MI increases with increasing impurity fraction and superfluid-impurity coupling strength. However, the tendency of a given BEC towards the MI decreases with the decreasing mass of the impurity atoms while the sign of the superfluid-impurity interaction plays no role. The above results are true even for attractive BECs except for a weak superfluid-impurity coupling, where the MI phenomenon is marginally suppressed by the presence of impurities. The dissipation of the solitons reduces their lifetime and is eminent for a larger impurity fraction and strong superfluid-impurity strength respectively., Comment: A new reference added, Accepted for publication in Phys. Lett. A 2023

By means of analytical and numerical methods, we address the modulational instability (MI) in chiral condensates governed by the Gross-Pitaevskiiequation including the current nonlinearity. The analysis shows that this nonlinearity partly suppresses off the MI driven by the cubic self-focusing, although the current nonlinearity is not represented in the system's energy (although it modifies the momentum), hence it may be considered as zero-energy nonlinearity. Direct simulations demonstrate generation of trains of stochastically interacting chiral solitons by MI. In the ring-shaped setup, the MI creates a single traveling solitary wave. The sign of the current nonlinearity determines the direction of propagation of the emerging solitons., Comment: 9 pages,8 figures, To be published in Physical Review E

We study modulation instability (MI) of flat states in two-component spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) in the framework of coupled Gross-Pitaevskii equations for two components of the pseudospinor wave function. The analysis is performed for equal densities of the components. Effects of the interaction parameters, Rabi coupling, and SOC on the MI are investigated. In particular, the results demonstrate that the SOC strongly alters the commonly known MI (immiscibility) condition, $g_{12} > g_{1} g_{2}$, for the binary superfluid with coefficients $g_{1,2}$ and $g_{12}$ of the intra- and interspecies repulsive interactions. In fact, the binary BEC is always subject to the MI under the action of the SOC, which implies that the ground state of the system is plausibly represented by a striped phase.

We obtain general continuous-wave (CW)\ solutions in the model of a spinor positronium condensate in the absence of magnetic field. The CW solutions with both in-phase ($n=0$) and out-of-phase ($n=1$) spin components exist, with their ranges limited by the total particle density, $\rho $. In the limit of negligible population exchange between the spin components, the CW solutions are found to be stable or unstable, depending on the particle density of the para positronium. Ortho positronium, in the $F=1$ spinor state, forms a ferromagnetic condensate with stable in-phase CW solutions only. Subsequent examination of the modulational instability (MI) is carried out both in the limit case of identical wavenumbers in the spin components, $% \Delta k\equiv k_{1}-k_{-1}=0$, and in the more general case of $\Delta k\neq 0$ too. The CW solutions with $n=0$ and $1$ solutions, which are stable in the case of $\Delta k=0$, are unstable for $\Delta k\neq 0$, for the natural repulsive sign of the nonlinearities. The total particle density, $\rho $, in the limit of $\Delta k=0$ is found to have a significant role for the stability of the condensate, which is determined by the sign of the self-interaction nonlinearity.