On the fluid approximation to a nonlinear Schrödinger equation

Nicholas Ercolani; Richard Montgomery

doi:10.1016/0375-9601(93)90290-G

On the fluid approximation to a nonlinear Schrödinger equation

Nicholas Ercolani, Richard Montgomery

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We present a heuristic proof that the nonlinear Schrödinger equation (NLS) - iθ{symbol}Ψ θ{symbol}t= 1 2ΔΨ+ 1 2(1-|Ψ|²)Ψ in 2 + 1 dimensions has a family of solutions which can be well approximated by a collection of point vortices for a planar incompressible fluid. The novelty of our approach is that we begin with a representation of the NLS as a compressible perturbation of Euler's equations for hydrodynamics.

Original language	English (US)
Pages (from-to)	402-408
Number of pages	7
Journal	Physics Letters A
Volume	180
Issue number	6
DOIs	https://doi.org/10.1016/0375-9601(93)90290-G
State	Published - Sep 20 1993

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1016/0375-9601(93)90290-G

Cite this

@article{5e939289e3ff4d28b3c863ae061e6baf,

title = "On the fluid approximation to a nonlinear Schr{\"o}dinger equation",

abstract = "We present a heuristic proof that the nonlinear Schr{\"o}dinger equation (NLS) - iθ\{symbol\}Ψ θ\{symbol\}t= 1 2ΔΨ+ 1 2(1-|Ψ|2)Ψ in 2 + 1 dimensions has a family of solutions which can be well approximated by a collection of point vortices for a planar incompressible fluid. The novelty of our approach is that we begin with a representation of the NLS as a compressible perturbation of Euler's equations for hydrodynamics.",

author = "Nicholas Ercolani and Richard Montgomery",

note = "Funding Information: Research supported by a grant from the NSF ( DMS-9001897 ) and by the AFOSR through the Arizona Center for Mathe-matical Sciences.",

year = "1993",

month = sep,

day = "20",

doi = "10.1016/0375-9601(93)90290-G",

language = "English (US)",

volume = "180",

pages = "402--408",

journal = "Physics Letters A",

issn = "0375-9601",

publisher = "Elsevier B.V.",

number = "6",

}

TY - JOUR

T1 - On the fluid approximation to a nonlinear Schrödinger equation

AU - Ercolani, Nicholas

AU - Montgomery, Richard

N1 - Funding Information: Research supported by a grant from the NSF ( DMS-9001897 ) and by the AFOSR through the Arizona Center for Mathe-matical Sciences.

PY - 1993/9/20

Y1 - 1993/9/20

N2 - We present a heuristic proof that the nonlinear Schrödinger equation (NLS) - iθ{symbol}Ψ θ{symbol}t= 1 2ΔΨ+ 1 2(1-|Ψ|2)Ψ in 2 + 1 dimensions has a family of solutions which can be well approximated by a collection of point vortices for a planar incompressible fluid. The novelty of our approach is that we begin with a representation of the NLS as a compressible perturbation of Euler's equations for hydrodynamics.

AB - We present a heuristic proof that the nonlinear Schrödinger equation (NLS) - iθ{symbol}Ψ θ{symbol}t= 1 2ΔΨ+ 1 2(1-|Ψ|2)Ψ in 2 + 1 dimensions has a family of solutions which can be well approximated by a collection of point vortices for a planar incompressible fluid. The novelty of our approach is that we begin with a representation of the NLS as a compressible perturbation of Euler's equations for hydrodynamics.

UR - http://www.scopus.com/inward/record.url?scp=0000002076&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000002076&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(93)90290-G

DO - 10.1016/0375-9601(93)90290-G

M3 - Article

AN - SCOPUS:0000002076

SN - 0375-9601

VL - 180

SP - 402

EP - 408

JO - Physics Letters A

JF - Physics Letters A

IS - 6

ER -

On the fluid approximation to a nonlinear Schrödinger equation

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this