Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation

Abstract

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the numerical solution. We have a two point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, are equal for large distances. In order to obtain fast convergence, the secant method is used.

2 figures

Cited by in corpus (38)

• Numerical Solution of the Gross-Pitaevskii Equation for Bose-Einstein Condensation
• Controlled Collapse of a Bose-Einstein Condensate
• Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap
• Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations
• Stability of trapped Bose-Einstein condensates
• Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional
• Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation
• Atomic Bose-Einstein Condensation with Three-Body Interactions and Collective Excitations
• Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps
• Numerical Solution of the Two-Dimensional Gross-Pitaevskii Equation for Trapped Interacting Atoms
• Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions
• Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap
• Critical numbers of attractive Bose-condensed atoms in asymmetric traps
• Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
• Mean-field description of collapsing and exploding Bose-Einstein condensates
• Stability analysis of the D-dimensional nonlinear Schroedinger equation with trap and two- and three-body interactions
• Coupled Bose-Einstein condensate: Collapse for attractive interaction
• Scaling limit of virtual states of triatomic systems
• Liquid-Gas phase transition in Bose-Einstein Condensates with time evolution
• Stability and Decay Rates of Non-Isotropic Attractive Bose-Einstein Condensates
• Autosolitons in trapped Bose-Einstein condensates with two- and three-body inelastic processes
• Bright solitary waves and trapped solutions in Bose-Einstein condensates with attractive interactions
• Conservation laws, bright matter wave solitons and modulational instability of nonlinear Schrödinger equation with time-dependent nonlinearity
• Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation
• Solitons under spatially localized cubic-quintic-septimal nonlinearities
• Domain wall suppression in trapped mixtures of Bose-Einstein condensates
• Localized modes in the Gross-Pitaevskii equation with a parabolic trapping potential and a nonlinear lattice pseudopotential
• Vortex Dynamics of Rotating Bose-Einstein Condensate of Microcavity Polaritons
• Limits of validity for a semiclassical mean-field two-fluid model for Bose-Einstein condensation thermodynamics
• Effect of anharmonicities in the critical number of trapped condensed atoms with attractive two-body interaction
• Bose-Einstein condensation thermodynamics of a trapped gas with attractive interaction
• Scattering of cold ${}^4$He on ${}^4$He${-}^{6,7}$Li and ${}^4$He${-}^{23}$Na molecules
• Exact solutions to the spin-2 Gross-Pitaevskii equations
• Nonlinear Klein-Gordon equation and the Bose-Einstein condensation
• Dynamics of Bose-Einstein condensates under anharmonic trap
• Diode effect in a skyrmion-coupled high-temperature Josephson junction
• Stability of dark solitons in a bubble Bose-Einstein condensate
• On non-existence of continuous families of stationary nonlinear modes for a class of complex potentials