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We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the…
We present variational calculations using a Gaussian trial function to calculate the ground state of the Gross-Pitaevskii equation and to describe the dynamics of the quasi-two-dimensional solitons in dipolar Bose-Einstein condensates.…
The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual…
We investigate the two-dimensional modified Gross-Pitaevskii equation, accounting for the effects of atom gain/loss and a time-independent isotropic confining potential, utilizing the Hirota's bilinear method. Through an appropriate…
We study the Bose-Einstein condensate trapped in a three-dimensional spherically symmetrical potential. Exact solutions to the stationary Gross-Pitaevskii equation are obtained for properly modulated radial nonlinearity. The solutions…
In this study, after we have briefly introduced the standard Gross-Pitaevskii equation, we have suggested fractional Gross-Pitaevskii equations to investigate the time-dependent ground state dynamics of the Bose-Einstein condensation of…
General soliton solutions to a nonlocal nonlinear Schr\"odinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions {are considered} via the combination of Hirota's bilinear method and the Kadomtsev-Petviashvili…
The Gross-Pitaevskii equation, or more generally the nonlinear Schr\"odinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the…
We study quantum double dark-solitons by constructing corresponding quantum states in the Lieb-Liniger model for the one-dimensional Bose gas. Here we expect that the Gross-Pitaevskii (GP) equation should play a central role in the long…
In this paper we consider the two-dimensional stochastic Gross-Pitaevskii equation, which is a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg-Landau equation with a harmonic…
A stochastic Gross-Pitaevskii equation is derived for partially condensed Bose gas systems subject to binary contact interactions. The theory we present provides a classical-field theory suitable for describing dissipative dynamics and…
Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double…
We report a novel algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent…
There have been many discussions of two-mode models for Bose condensates in a double well potential, but few cases in which parameters for these models have been calculated for realistic situations. Recent experiments lead us to use the…
We are concerned with the following system of two coupled time-independent Gross-Pitaevskii equations $$ \begin{cases} -\Delta u+\lambda_1 u=\mu_1|u|^{p-2}u+\nu\alpha |u|^{\alpha-2}|v|^{\beta}u ~\hbox{in}~ \R^N,\\ -\Delta v+\lambda_2…
We extend one component Gross-Pitaevskii equation to two component coupled case with the damping term, linear and parabolic density profiles, then give the Lax pair and infinitely-many conservations laws of this coupled system. The system…
Bose condensation of interacting bosons in a two-dimensional random potential is studied. The Gross-Pitaevskii equation is solved to determine the spatially-varying order parameter and the localization length as a function of the disorder,…
We study the general (2+1)-dimensional Davey-Stewartson (DS) equations with nonlinear and gain terms and acquire explicit solutions through variable separation approach. In particular, we deduce some main novel excitations for the DS…
The stochastic Gross-Pitaevskii equation represents a versatile approach for studying the dynamics of trapped degenerate ultracold Bose gases in the presence of large phase and density fluctuations. Following a brief review of the original…
A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the…