相关论文: Bose-Einstein Condensates and spectral properties …
We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended Non-linear sigma model (NLSM) like…
We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a…
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…
In this paper we study the existence of solutions to nonlinear Schr\"odinger systems with mixed couplings of attractive and repulsive forces, which arise from the models in Bose-Einstein condensates and nonlinear optics. In particular, we…
The modulational instability and discrete matter wave solitons in dipolar BEC, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instability of nonlinear plane matter waves in a…
A self consistent theory of a cigar shaped Bose-Einstein condensate (BEC) periodically modulated by a laser beam is presented. We show, both theoretically and numerically, that modulational instability/stability is the mechanism by which…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box or periodic boundary conditions are presented in analytic form for the case of attractive nonlinearity. A companion paper has treated the repulsive…
We study the spatiotemporal Bloch states of a high-frequency driven two-component Bose-Einstein condensate (BEC) with spin-orbit coupling (SOC) in an optical lattice. By adopting the rotating-wave approximation (RWA) and applying an exact…
We study soliton solutions to a nonlinear Schrodinger equation with a saturated nonlinearity. Such nonlinearities are known to possess minimal mass soliton solutions. We consider a small perturbation of a minimal mass soliton, and identify…
In this work, we explore systematically various SO(2)-rotation-induced multiple dark-dark soliton breathing patterns obtained from stationary and spectrally stable multiple dark-bright and dark-dark waveforms in trapped one-dimensional,…
The modulational stability of the nonlinear Schr{\"o}dinger (NLS) equation is examined in the case with a quadratic external potential. This study is motivated by recent experimental studies in the context of matter waves in Bose-Einstein…
The dynamics of Bose-Einstein condensates in the lowest energy band of a one-dimensional optical lattice is generally disturbed by the presence of transversally excited resonant states. We propose an effective one-dimensional theory which…
We use the mathematical toolbox of the inverse scattering transform to study quantitatively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schr{\"o}dinger equation. We present a…
The connection between quantized vortices and dark solitons in a long and thin, waveguide-like trap geometry is explored in the framework of the non-linear Schr\"odinger equation. Variation of the transverse confinement leads from the…
We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the…
The occurrence of a molecular Bose-Einstein condensate is studied for an atomic system near a zero energy resonance of the binary scattering process, with a large and positive scattering length. The interaction potential is modeled by a…
The long-time asymptotic behavior of solutions to the focusing nonlinear Schr\"odinger (NLS) equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the case of initial conditions that allow for the…
We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky (GP) equation with a periodic potential, we employ an envelope…
Important information for the roton-maxon spectrum of a flattened dipolar Bose-Einstein condensate is extracted by applying a static perturbation exhibiting a periodic in-plane modulation. By solving the Gross-Pitaevskii equation in the…
In this paper we consider a two component system of coupled non linear Schr\"odinger equations modeling the phase separation in the binary mixture of Bose-Einstein condensates and other related problems. Assuming the existence of solutions…