Related papers: Wave modes trapped in rotating nonlinear potential…
We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the…
Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary…
We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function…
Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal…
We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schr\"odinger and the Maxwell-Bloch equations. We find that prolific different types of nonlinear localized and…
In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrodinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of…
We study the instability of a ring Bose-Einstein condensate under a periodic modulation of inter-atomic interactions. The condensate exhibits temporal and spatial patterns induced by the parametric resonance, which can be characterized by…
We consider the 3D cubic nonlinear Schr\"odinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of global solutions to the time-dependent model can be described…
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
We demonstrate the stabilization of two-dimensional nonlinear wave patterns by means of a dissipative confinement potential. Our analytical and numerical analysis, based on the generalized dissipative Gross-Pitaevskii equation, makes use of…
By means of the variational method and numerical simulations, we demonstrate the existence of stable 3D nonlinear modes, viz. vortex ``bullets'', in the form of pulsed beams carrying orbital angular momentum, that can self-trap in a 2D…
We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering…
Using a focused laser beam we stir a Bose-Einstein condensate confined in a magnetic trap. When the stirring frequency lies near the transverse quadrupolar mode resonance we observe the nucleation of vortices. When several vortices are…
We study the long-time behavior of solutions to the nonlinear Schr\"odinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric double-well potential, continuing work of the 2nd and 3rd authors. NLS/GP governs nearly-monochromatic guided…
We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and…
We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensate in a rotating double-well trap potential and co-rotating optical lattice. We show that, in agreement with the experiment, the vortex number do not diverge…
Nonlinearity in the Schr\"odinger equation gives rise to rich phenomena such as soliton formation, modulational instability, and self-organization in diverse physical systems. Motivated by recent advances in engineering nonlinear gauge…
The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial…
We develop a multimode model that describes the dynamics on a rotating Bose-Einstein condensate confined by a ring-shaped optical lattice with large filling numbers. The parameters of the model are obtained as a function of the rotation…