Nonlinear Dynamics

, Volume 88, Issue 4, pp 2957–2967 | Cite as

Tunneling dynamics between atomic bright solitons

  • Li-Chen Zhao
  • Liming Ling
  • Zhan-Ying Yang
  • Wen-Li Yang
Original Paper


We investigate tunneling behavior between two bright solitons in a Bose–Einstein condensate with attractive contact interactions between atoms. The explicit tunneling properties including tunneling particles and oscillation period are described analytically, which indicates that the periodic tunneling form is a nonlinear Josephson type oscillation. The results suggest that the breathing behavior of solitons comes from the tunneling mechanism in an effective double-well potential, which is quite different from the modulational instability mechanism for Akhmediev breather and K-M breather. The relative phase between the two solitons has no effects on the tunneling period and particle exchanging rate. Furthermore, we obtain a phase diagram for two-soliton interaction which admits tunneling property, particle-like property, interference property, and a resonant interaction case. The explicit conditions for them are clarified based on the defined critical distance \(d_c\) and spatial interference period D.


Soliton tunneling Wave properties Particle properties 



This work is supported by National Natural Science Foundation of China (Contact No. 11405129, 11404259), and Shaanxi Province Science association of colleges and universities (Contact No. 20160216).


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.School of PhysicsNorthwest UniversityXi’anChina
  2. 2.Shaanxi Key Laboratory for Theoretical Physics FrontiersXi’anChina
  3. 3.School of MathematicsSouth China University of TechnologyGuangzhouChina
  4. 4.Institute of Modern PhysicsNorthwest UniversityXianChina

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