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.
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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 -