Chiquillo, Emerson 2017. Harmonically trapped attractive and repulsive spin–orbit and Rabi coupled Bose–Einstein condensates. Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue. 10, p. 105001.
Tang, Qinglin Zhang, Yong and Mauser, Norbert J. 2017. A robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose–Einstein condensates. Computer Physics Communications, Vol. 219, p. 223.
Antoine, Xavier Besse, Christophe Duboscq, Romain and Rispoli, Vittorio 2017. Acceleration of the imaginary time method for spectrally computing the stationary states of Gross–Pitaevskii equations. Computer Physics Communications, Vol. 219, p. 70.
Wu, Xinming Wen, Zaiwen and Bao, Weizhu 2017. A Regularized Newton Method for Computing Ground States of Bose–Einstein Condensates. Journal of Scientific Computing, Vol. 73, Issue. 1, p. 303.
Antoine, Xavier Levitt, Antoine and Tang, Qinglin 2017. Efficient spectral computation of the stationary states of rotating Bose–Einstein condensates by preconditioned nonlinear conjugate gradient methods. Journal of Computational Physics, Vol. 343, p. 92.
Wang, Tingchun 2017. A linearized, decoupled, and energy-preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations. Numerical Methods for Partial Differential Equations, Vol. 33, Issue. 3, p. 840.
Guo, Yujin Zeng, Xiaoyu and Zhou, Huan-Song 2017. Blow-up solutions for two coupled Gross-Pitaevskii equations with attractive interactions. Discrete and Continuous Dynamical Systems, Vol. 37, Issue. 7, p. 3749.
Dias, João-Paulo Figueira, Mário and Konotop, Vladimir V. 2016. Coupled Nonlinear Schrödinger Equations with a Gauge Potential: Existence and Blowup. Studies in Applied Mathematics, Vol. 136, Issue. 3, p. 241.
Chiquillo, Emerson 2015. Matter-waves in Bose–Einstein condensates with spin-orbit and Rabi couplings. Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue. 47, p. 475001.
Liu, Baiyu and Ma, Li 2015. Blow up threshold for the Gross–Pitaevskii system with combined nonlocal nonlinearities. Journal of Mathematical Analysis and Applications, Vol. 425, Issue. 2, p. 1214.
Bao, Weizhu and Cai, Yongyong 2015. Ground States and Dynamics of Spin-Orbit-Coupled Bose--Einstein Condensates. SIAM Journal on Applied Mathematics, Vol. 75, Issue. 2, p. 492.
Wang, Tingchun 2015. Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator. Journal of Mathematical Analysis and Applications, Vol. 422, Issue. 1, p. 286.
Wang, Tingchun 2014. Optimal Point-Wise Error Estimate of a Compact Difference Scheme for the Coupled Gross–Pitaevskii Equations in One Dimension. Journal of Scientific Computing, Vol. 59, Issue. 1, p. 158.
Wang, Hanquan and Xu, Zhiguo 2014. Projection gradient method for energy functional minimization with a constraint and its application to computing the ground state of spin–orbit-coupled Bose–Einstein condensates. Computer Physics Communications, Vol. 185, Issue. 11, p. 2803.
Wang, TingChun and Zhao, XiaoFei 2014. Optimal l ∞ error estimates of finite difference methods for the coupled Gross-Pitaevskii equations in high dimensions. Science China Mathematics, Vol. 57, Issue. 10, p. 2189.
Antoine, Xavier and Duboscq, Romain 2014. GPELab, a Matlab toolbox to solve Gross–Pitaevskii equations I: Computation of stationary solutions. Computer Physics Communications, Vol. 185, Issue. 11, p. 2969.
Jin, Jingjing Zhang, Suying and Han, Wei 2014. Zero-momentum coupling induced transitions of ground states in Rashba spin–orbit coupled Bose–Einstein condensates. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 47, Issue. 11, p. 115302.
Ming, Ju Tang, Qinglin and Zhang, Yanzhi 2014. An efficient spectral method for computing dynamics of rotating two-component Bose–Einstein condensates via coordinate transformation. Journal of Computational Physics, Vol. 258, p. 538.
Wang, Hanquan 2014. A projection gradient method for computing ground state of spin-2 Bose–Einstein condensates. Journal of Computational Physics, Vol. 274, p. 473.
Chern, I-Liang and Lin, Liren 2014. A kinetic energy reduction technique and characterizations of the ground states of spin-1 Bose-Einstein condensates. Discrete and Continuous Dynamical Systems - Series B, Vol. 19, Issue. 4, p. 1119.
In this paper, we prove existence and uniqueness results for the ground states of the coupled Gross-Pitaevskii equations for describing two-component Bose-Einstein condensates with an internal atomic Josephson junction, and obtain the limiting behavior of the ground states with large parameters. Efficient and accurate numerical methods based on continuous normalized gradient flow and gradient flow with discrete normalization are presented, for computing the ground states numerically. A modified backward Euler finite difference scheme is proposed to discretize the gradient flows. Numerical results are reported, to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomena of the ground sates in the problem.
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