Geometric Optics for One-Dimensional Schrödinger-Poisson System

Zhifei Zhang; Qionglei Chen

doi:10.1007/s11401-004-0074-8

Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (3) : 353 -362. DOI: 10.1007/s11401-004-0074-8

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Geometric Optics for One-Dimensional Schrödinger-Poisson System

Zhifei Zhang ¹^,a
, Qionglei Chen ²

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Abstract

This paper considers a family of Schrödinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of the solution outside the caustic, and near the caustic.

Keywords

Shrödinger-Poisson / Geometric optics / Lagrangian integral / 35Q55

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Zhifei Zhang, Qionglei Chen. Geometric Optics for One-Dimensional Schrödinger-Poisson System. Chinese Annals of Mathematics, Series B, 2006, 27(3): 353-362 DOI:10.1007/s11401-004-0074-8

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