A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates

Juan J. García-Ripoll; Vladimir V. Konotop; Boris Malomed; Víctor M. Pérez-García

doi:10.1016/S0378-4754(02)00190-8

A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates

Juan J. García-Ripoll^*
, Vladimir V. Konotop
, Boris Malomed
, Víctor M. Pérez-García

^*Corresponding author for this work

Engineering General

Research output: Contribution to journal › Conference article › peer-review

60 Scopus citations

Abstract

We study a quasi-local approximation for a nonlocal nonlinear Schrödinger equation. The problem is closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. The nonlocality is approximated by a nonlinear dispersion term, which is controlled by physically meaningful parameters. We show that the phenomenology found in the nonlocal model is very similar to that present in the reduced one with the nonlinear dispersion. We prove rigorously the absence of collapse in the model, and obtain numerically its stable soliton-like ground state.

Original language	English
Pages (from-to)	21-30
Number of pages	10
Journal	Mathematics and Computers in Simulation
Volume	62
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-4754(02)00190-8
State	Published - 13 Feb 2003
Event	Nonlinear Waves: Computation and Theory II - Athens, GE, United States Duration: 9 Apr 2001 → 12 Apr 2001

Funding

Funders	Funder number
Comisión Interministerial de Ciencia y Tecnología	DGCYT-HP1999-019, BFM2000-0521

Keywords

Blow-up phenomena
Bose-Einstein condensation
Nonlinear waves

Access to Document

10.1016/S0378-4754(02)00190-8

Cite this

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title = "A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates",

abstract = "We study a quasi-local approximation for a nonlocal nonlinear Schr{\"o}dinger equation. The problem is closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. The nonlocality is approximated by a nonlinear dispersion term, which is controlled by physically meaningful parameters. We show that the phenomenology found in the nonlocal model is very similar to that present in the reduced one with the nonlinear dispersion. We prove rigorously the absence of collapse in the model, and obtain numerically its stable soliton-like ground state.",

keywords = "Blow-up phenomena, Bose-Einstein condensation, Nonlinear waves",

author = "Garc{\'i}a-Ripoll, \{Juan J.\} and Konotop, \{Vladimir V.\} and Boris Malomed and P{\'e}rez-Garc{\'i}a, \{V{\'i}ctor M.\}",

note = "Funding Information: JJG-R and VMP-G have been supported by CICYT under grant BFM2000-0521. The cooperative work has been supported through the bilateral program DGCYT-HP1999-019/A{\c c}{\~a}o no. E-89/00.; Nonlinear Waves: Computation and Theory II ; Conference date: 09-04-2001 Through 12-04-2001",

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doi = "10.1016/S0378-4754(02)00190-8",

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T1 - A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates

AU - García-Ripoll, Juan J.

AU - Konotop, Vladimir V.

AU - Malomed, Boris

AU - Pérez-García, Víctor M.

N1 - Funding Information: JJG-R and VMP-G have been supported by CICYT under grant BFM2000-0521. The cooperative work has been supported through the bilateral program DGCYT-HP1999-019/Ação no. E-89/00.

PY - 2003/2/13

Y1 - 2003/2/13

N2 - We study a quasi-local approximation for a nonlocal nonlinear Schrödinger equation. The problem is closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. The nonlocality is approximated by a nonlinear dispersion term, which is controlled by physically meaningful parameters. We show that the phenomenology found in the nonlocal model is very similar to that present in the reduced one with the nonlinear dispersion. We prove rigorously the absence of collapse in the model, and obtain numerically its stable soliton-like ground state.

AB - We study a quasi-local approximation for a nonlocal nonlinear Schrödinger equation. The problem is closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. The nonlocality is approximated by a nonlinear dispersion term, which is controlled by physically meaningful parameters. We show that the phenomenology found in the nonlocal model is very similar to that present in the reduced one with the nonlinear dispersion. We prove rigorously the absence of collapse in the model, and obtain numerically its stable soliton-like ground state.

KW - Blow-up phenomena

KW - Bose-Einstein condensation

KW - Nonlinear waves

UR - https://www.scopus.com/pages/publications/0037434584

U2 - 10.1016/S0378-4754(02)00190-8

DO - 10.1016/S0378-4754(02)00190-8

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AN - SCOPUS:0037434584

SN - 0378-4754

VL - 62

SP - 21

EP - 30

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

IS - 1-2

T2 - Nonlinear Waves: Computation and Theory II

Y2 - 9 April 2001 through 12 April 2001

ER -

A quasi-local Gross-Pitaevskii equation for attractive Bose-Einstein condensates

Abstract

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Keywords

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