TY - JOUR

T1 - Stationary solutions of the Gross-Pitaevskii equation with linear counterpart

AU - D'Agosta, Roberto

AU - Malomed, Boris A.

AU - Presilla, Carlo

PY - 2000/10/23

Y1 - 2000/10/23

N2 - We study the stationary solutions of the Gross-Pitaevskii equation that reduce, in the limit of vanishing non-linearity, to the eigenfunctions of the associated Schrodinger equation. By providing analytical and numerical support, we conjecture an existence condition for these solutions in terms of the ratio between their proper frequency (chemical potential) and the corresponding linear eigenvalue. We also give approximate expressions for the stationary solutions which become exact in the opposite limit of strong non-linearity. For one-dimensional systems these solutions have the form of a chain of dark or bright solitons depending on the sign of the non-linearity. We demonstrate that in the case of negative non-linearity (attractive interaction) the norm of the solutions is always bounded for dimensions greater than one. (C) 2000 Elsevier Science B.V.

AB - We study the stationary solutions of the Gross-Pitaevskii equation that reduce, in the limit of vanishing non-linearity, to the eigenfunctions of the associated Schrodinger equation. By providing analytical and numerical support, we conjecture an existence condition for these solutions in terms of the ratio between their proper frequency (chemical potential) and the corresponding linear eigenvalue. We also give approximate expressions for the stationary solutions which become exact in the opposite limit of strong non-linearity. For one-dimensional systems these solutions have the form of a chain of dark or bright solitons depending on the sign of the non-linearity. We demonstrate that in the case of negative non-linearity (attractive interaction) the norm of the solutions is always bounded for dimensions greater than one. (C) 2000 Elsevier Science B.V.

UR - http://www.scopus.com/inward/record.url?scp=0034706482&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(00)00619-8

DO - 10.1016/S0375-9601(00)00619-8

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AN - SCOPUS:0034706482

SN - 0375-9601

VL - 275

SP - 424

EP - 434

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 5-6

ER -