TY - JOUR

T1 - On the fluid approximation to a nonlinear Schrödinger equation

AU - Ercolani, Nicholas

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.

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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 -