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

Mathematics

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

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10.1016/0375-9601(93)90290-G

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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.",

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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.

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

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JO - Physics Letters A

JF - Physics Letters A

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On the fluid approximation to a nonlinear Schrödinger equation

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