For the system -Delta U-i + U-i = U-i(3) - beta U-i Sigma U-j not equal i(j)2, i = 1,...,k, (with k >= 3), we prove the existence for beta large of positive radial solutions on R-N. We show that as beta -> +infinity, 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 -Delta W + W = W-3. 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.
Terracini, S., Verzini, G. (2009). Multipulse phases in k-mixtures of Bose-einstein condensates. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 194(3), 717-741 [10.1007/s00205-008-0172-y].
Multipulse phases in k-mixtures of Bose-einstein condensates
TERRACINI, SUSANNA;
2009
Abstract
For the system -Delta U-i + U-i = U-i(3) - beta U-i Sigma U-j not equal i(j)2, i = 1,...,k, (with k >= 3), we prove the existence for beta large of positive radial solutions on R-N. We show that as beta -> +infinity, 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 -Delta W + W = W-3. 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.
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