Archive for Rational Mechanics and Analysis

, Volume 194, Issue 3, pp 717–741 | Cite as

Multipulse Phases in k-Mixtures of Bose–Einstein Condensates

  • Susanna TerraciniEmail author
  • Gianmaria Verzini


For the system
$$-\Delta U_i+ U_i=U_i^3-\beta U_i\sum_{j\neq i}U_j^2,\quad i=1,\dots,k,$$
(with k ≧ 3), we prove the existence for β large of positive radial solutions on \({\mathbb R^N}\) . We show that as β →  + ∞, the profile of each component U i separates, in many pulses, from the others. Moreover, we can prescribe the location of such pulses in terms of the oscillations of the changing-sign solutions of the scalar equation  − ΔW  +  W  =  W3. Within an Hartree–Fock approximation, this provides a theoretical indication of phase separation into many nodal domains for the k-mixtures of Bose–Einstein condensates.


Solitary Wave Implicit Function Theorem Einstein Condensate Radial Solution Nodal Domain 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano-BicoccaMilanItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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