American Institute of Mathematical Sciences

Advanced
May  2003, 3(2): 179-192. doi: 10.3934/dcdsb.2003.3.179

Exact solution of the two-mode model of multicomponent Bose-Einstein condensates

Vadym Vekslerchik 1, and  Víctor M. Pérez-García 1,

1. 

Departamento de Matemáticas, E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain, Spain

Received  March 2002 Revised  January 2003 Published  February 2003

We find the explicit solution of the so-called two-mode model for multicomponent Bose-Einstein condensates. We prove that all the solutions are constants or periodic functions and give explicit formulae for them.
Keywords: Nonlinear waves, Bose-Einstein condensation., exactly solvable models.
Mathematics Subject Classification: 74J30, 34A05, 35Q55, 37N2.
Citation: Vadym Vekslerchik, Víctor M. Pérez-García. Exact solution of the two-mode model of multicomponent Bose-Einstein condensates. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 179-192. doi: 10.3934/dcdsb.2003.3.179
[1]

Weizhu Bao, Yongyong Cai. Mathematical theory and numerical methods for Bose-Einstein condensation. Kinetic & Related Models, 2013, 6 (1) : 1-135. doi: 10.3934/krm.2013.6.1
[2]

Anne de Bouard, Reika Fukuizumi, Romain Poncet. Vortex solutions in Bose-Einstein condensation under a trapping potential varying randomly in time. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 2793-2817. doi: 10.3934/dcdsb.2015.20.2793
[3]

Vladimir S. Gerdjikov. Bose-Einstein condensates and spectral properties of multicomponent nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1181-1197. doi: 10.3934/dcdss.2011.4.1181
[4]

José A. Carrillo, Katharina Hopf, Marie-Therese Wolfram. Numerical study of Bose–Einstein condensation in the Kaniadakis–Quarati model for bosons. Kinetic & Related Models, 2020, 13 (3) : 507-529. doi: 10.3934/krm.2020017
[5]

Xuguang Lu. Long time strong convergence to Bose-Einstein distribution for low temperature. Kinetic & Related Models, 2018, 11 (4) : 715-734. doi: 10.3934/krm.2018029
[6]

Florian Méhats, Christof Sparber. Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5097-5118. doi: 10.3934/dcds.2016021
[7]

P.G. Kevrekidis, Dimitri J. Frantzeskakis. Multiple dark solitons in Bose-Einstein condensates at finite temperatures. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1199-1212. doi: 10.3934/dcdss.2011.4.1199
[8]

Weizhu Bao, Loïc Le Treust, Florian Méhats. Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime. Kinetic & Related Models, 2017, 10 (3) : 553-571. doi: 10.3934/krm.2017022
[9]

Pedro J. Torres, R. Carretero-González, S. Middelkamp, P. Schmelcher, Dimitri J. Frantzeskakis, P.G. Kevrekidis. Vortex interaction dynamics in trapped Bose-Einstein condensates. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1589-1615. doi: 10.3934/cpaa.2011.10.1589
[10]

Brahim Alouini, Olivier Goubet. Regularity of the attractor for a Bose-Einstein equation in a two dimensional unbounded domain. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 651-677. doi: 10.3934/dcdsb.2014.19.651
[11]

Brahim Alouini. Long-time behavior of a Bose-Einstein equation in a two-dimensional thin domain. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1629-1643. doi: 10.3934/cpaa.2011.10.1629
[12]

Brahim Alouini. Finite dimensional global attractor for a Bose-Einstein equation in a two dimensional unbounded domain. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1781-1801. doi: 10.3934/cpaa.2015.14.1781
[13]

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
[14]

Liren Lin, I-Liang Chern. A kinetic energy reduction technique and characterizations of the ground states of spin-1 Bose-Einstein condensates. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1119-1128. doi: 10.3934/dcdsb.2014.19.1119
[15]

Kui Li, Zhitao Zhang. A perturbation result for system of Schrödinger equations of Bose-Einstein condensates in $\mathbb{R}^3$. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 851-860. doi: 10.3934/dcds.2016.36.851
[16]

Yongming Luo, Athanasios Stylianou. On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020239
[17]

Jerry L. Bona, Henrik Kalisch. Models for internal waves in deep water. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 1-20. doi: 10.3934/dcds.2000.6.1
[18]

Elena Kartashova. Nonlinear resonances of water waves. Discrete & Continuous Dynamical Systems - B, 2009, 12 (3) : 607-621. doi: 10.3934/dcdsb.2009.12.607
[19]

Angelo Morro. Nonlinear waves in thermoelastic dielectrics. Evolution Equations & Control Theory, 2019, 8 (1) : 149-162. doi: 10.3934/eect.2019009
[20]

J. M. Cushing. Nonlinear semelparous Leslie models. Mathematical Biosciences & Engineering, 2006, 3 (1) : 17-36. doi: 10.3934/mbe.2006.3.17

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (25)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences