# American Institute of Mathematical Sciences

July  2019, 24(7): 3175-3193. doi: 10.3934/dcdsb.2018306

## Bifurcation solutions of Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates

 1 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China 2 College of Science, Southwest Petroleum University, Chengdu, Sichuan 610500, China

* Corresponding author: Ruikuan Liu

Received  July 2018 Revised  July 2018 Published  October 2018

Fund Project: The work was supported by the Young Scholars Development Fund of SWPU (Grant No. 201899010079), and by the Natural Science Foundation of China (11771306)

The main aim of this paper is to study the bifurcation solutions associated with the spinor Bose-Einstein condensates. Based on the Principle of Hamilton Dynamics and the Principle of Lagrangian Dynamics, a general pattern formation equation for the spinor Bose-Einstein condensates is established. Moreover, three kinds of critical conditions for eigenvalues are obtained under spectrum analysis and the different external confining potentials. With the change of different external potentials, the different topological structures of bifurcation solutions for the spinor Bose-Einstein condensates system are derived from steady state bifurcation theory.

Citation: Dong Deng, Ruikuan Liu. Bifurcation solutions of Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3175-3193. doi: 10.3934/dcdsb.2018306
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##### References:
The graph of the part of S2
The graph of S1
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