Adhikari, "Fortran programs for the time-dependent Gross-Pitaevskii equation
in a fully anisotropic trap," Computer Physics Communications, vol.
Then in the mean-field approximation (in case when we neglect the contribution of the excited states) the BEC is described by the Gross-Pitaevskii equation
Consider the two-dimensional Gross-Pitaevskii Equation
Lakshmanan, "Bright and dark solitons in a quasi-1D Bose-Einstein condensates modelled by 1D GRoss-Pitaevskii equation
with timedependent parameters," Physica D: Nonlinear Phenomena, vol.
Recently, by using the Darboux dressing technique or Hirotas bilinear method, rogue waves solutions in complex system were obtained such as nonlinear Schrodinger equation, Hirota equation, Sasa-Satsuma equation, Davey-Stewartson equation, coupled Gross-Pitaevskii equation
, coupled NLS Maxwell-Bloch equation, and coupled Schrodinger-Boussinesq equation [15-26].
Among specific topics are a license plate recognition algorithm based on radial basis function neural networks, fabric weave design based on cellular automata theory, the experimental education of technical courses in the information age, learning causal semantic representation from information extraction, a symplectic scheme of the Gross-Pitaevskii equation
, and a humanoid intelligent control system of plastic corrugated board synchronous shearing.
In the subsequent section, we also discuss plausible extension of this gravitational Schrodinger equation to include the effect of phion condensate via Gross-Pitaevskii equation
, as described recently by Moffat.
Malomed, "Two-dimensional solitons in the Gross-Pitaevskii equation
with spatially modulated nonlinearity," Physical Review E, vol.
 used a simple Dufort-Frankel type scheme for solving the time-dependent Gross-Pitaevskii equation
. In this paper, we will use the Dufort-Frankel scheme to solve two-dimensional sine-Gordon equation.
The Gross-Pitaevskii equation
is a model for phenomena such as the Bose-Einstein condensation of ultra cold atomic gases, or the dark solitons of nonlinear optics.
In turn we provide a route where Maxwell equations and Schrodinger equation could be deduced from Gross-Pitaevskii equation
by using known algebra involving bi-quaternion number.