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Bifurcation analysis of stationary solutions of two-dimensional coupled Gross–Pitaevskii equations using deflated continuation

E. G. Charalampidis, Nicolas Boullé, Patrick E. Farrell +1 more

arXiv:1912.00023Communications in Nonlinear Science and Numerical SimulationMar 9, 202028 citations

Stability analysis and continuation for the coupled Gross–Pitaevskii equations

Sirilak Sriburadet, Yin-Tzer Shih, C.‐S. Chien

Computers & Mathematics with ApplicationsMar 13, 20193 citations

Continuation and stability analysis for Bloch waves of the Gross-Pitaevskii equation

H.-S. Chen, S.-L. Chang, B.‐W. Jeng +1 more

Numerical AlgorithmsMay 26, 20173 citations

Nonlinear waves in the Pitaevskii-Gross equation

Toshio Tsuzuki

Journal of Low Temperature PhysicsApr 1, 1971226 citations

Stationary solutions of Gross-Pitaevskii equations in a double square well

Weidong Li

We present analytical stationary solutions for the Gross-Pitaevskii equation (GPE) of a Bose-Einstein condensate (BECs) trapped in a double-well potential. These solutions are compared to those described by [Mahmud et al., Phys. Rev. A 66, 063607 (2002)]. In particular, we provide further evidence that symmetry preserving stationary solutions can be reduced to the eigenstates of the corresponding linear Schr\"odinger equation. Moreover, we have found that the symmetry-breaking solutions can emerge not only from bifurcations, but also from isolated points in the chemical potential--nonlinear interaction diagram. We also have found that there are some moving nodes in the symmetry-breaking solutions.We present analytical stationary solutions for the Gross-Pitaevskii equation (GPE) of a Bose-Einstein condensate (BECs) trapped in a double-well potential. These solutions are compared to those described by [Mahmud et al., Phys. Rev. A 66, 063607 (2002)]. In particular, we provide further evidence that symmetry preserving stationary solutions can be reduced to the eigenstates of the corresponding linear Schr\"odinger equation. Moreover, we have found that the symmetry-breaking solutions can emerge not only from bifurcations, but also from isolated points in the chemical potential--nonlinear interaction diagram. We also have found that there are some moving nodes in the symmetry-breaking solutions.

arXiv:cond-mat/0609340Physical Review ADec 11, 200620 citations

The symmetry breaking states and bifurcation of Bose–Einstein condensates in a double well

XinYan Jia, Weidong Li, Hiroshi Ezawa

An analytical approximation method to clarify the symmetry-breaking stationary solutions to the Gross–Pitaevskii equation with symmetric double-well external potential is presented. By this method, we can understand that each symmetry-breaking solution bifurcates from a symmetry-preserving solution as one varies the coupling constant of the nonlinear interaction, and predict the bifurcation point. Also, the method gives a good approximation to the energy eigenvalues of the lower states, symmetry-breaking as well as symmetry-preserving, as long as the nonlinear interaction is not too strong.An analytical approximation method to clarify the symmetry-breaking stationary solutions to the Gross–Pitaevskii equation with symmetric double-well external potential is presented. By this method, we can understand that each symmetry-breaking solution bifurcates from a symmetry-preserving solution as one varies the coupling constant of the nonlinear interaction, and predict the bifurcation point. Also, the method gives a good approximation to the energy eigenvalues of the lower states, symmetry-breaking as well as symmetry-preserving, as long as the nonlinear interaction is not too strong.

Journal of Physics A Mathematical and TheoreticalMay 22, 20071 citation

Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross—Pitaevskii Equation

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