### 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 | |

State | Published - Sep 20 1993 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

*180*(6), 402-408. https://doi.org/10.1016/0375-9601(93)90290-G

**On the fluid approximation to a nonlinear Schrödinger equation.** / Ercolani, Nicholas M; Montgomery, Richard.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 180, no. 6, pp. 402-408. https://doi.org/10.1016/0375-9601(93)90290-G

}

TY - JOUR

T1 - On the fluid approximation to a nonlinear Schrödinger equation

AU - Ercolani, Nicholas M

AU - Montgomery, Richard

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

VL - 180

SP - 402

EP - 408

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

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

SN - 0375-9601

IS - 6

ER -