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Fortran programs for the time-dependent Gross–Pitaevskii equation in a fully anisotropic trap. Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross–Pitaevskii (GP) equation describing the properties of Bose–Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank–Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all).


References in zbMATH (referenced in 16 articles )

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  1. Barna, Imre F.; Pocsai, Mihály A.; Mátyás, L.: Self-similarity analysis of the nonlinear Schrödinger equation in the Madelung form (2018)
  2. Kuang, Yang; Hu, Guanghui: An adaptive FEM with ITP approach for steady Schrödinger equation (2018)
  3. Luis E. Young-S.; Paulsamy Muruganandam; Sadhan K. Adhikari; Vladimir Loncar; Dusan Vudragovic; Antun Balaz: OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross-Pitaevskii equation (2017) arXiv
  4. Vinayagam, P. S.; Radha, R.; Bhuvaneswari, S.; Ravisankar, R.; Muruganandam, P.: Bright soliton dynamics in spin orbit-Rabi coupled Bose-Einstein condensates (2017)
  5. Young-S., Luis E.; Muruganandam, Paulsamy; Adhikari, Sadhan K.; Lončar, Vladimir; Vudragović, Dušan; Balaž, Antun: OpenMP GNU and intel Fortran programs for solving the time-dependent Gross-Pitaevskii equation (2017)
  6. Marojević, Želimir; Göklü, Ertan; Lämmerzahl, Claus: ATUS-PRO: a FEM-based solver for the time-dependent and stationary Gross-Pitaevskii equation (2016)
  7. Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric: A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation (2016)
  8. Young-S., Luis E.; Vudragović, Dušan; Muruganandam, Paulsamy; Adhikari, Sadhan K.; Balaž, Antun: OpenMP Fortran and C programs for solving the time-dependent Gross-Pitaevskii equation in an anisotropic trap (2016)
  9. Kishor Kumar, R.; Young-S., Luis E.; Vudragović, Dušan; Balaž, Antun; Muruganandam, Paulsamy; Adhikari, S. K.: Fortran and C programs for the time-dependent dipolar Gross-Pitaevskii equation in an anisotropic trap (2015)
  10. Moxley, Frederick Ira; Byrnes, Tim; Ma, Baoling; Yan, Yun; Dai, Weizhong: A G-FDTD scheme for solving multi-dimensional open dissipative Gross-Pitaevskii equations (2015)
  11. Antoine, Xavier; Duboscq, Romain: GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations. I: Computation of stationary solutions (2014)
  12. Luo, Ji: Nonlinear Schrödinger equation containing the time-derivative of the probability density: a numerical study (2014)
  13. Bao, Weizhu; Tang, Qinglin; Xu, Zhiguo: Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation (2013)
  14. Vudragović, Dušan; Vidanović, Ivana; Balaž, Antun; Muruganandam, Paulsamy; Adhikari, Sadhan K.: C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap (2012)
  15. Malomed, Boris A.; Nascimento, V. A.; Adhikari, Sadhan K.: Gap solitons in fermion superfluids (2009)
  16. Muruganandam, Paulsamy; Adhikari, Sadhan K.: Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap (2009)