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›› 2005, Vol. 22 ›› Issue (5): 639-644.DOI: 10.7523/j.issn.2095-6134.2005.5.014

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Studies on Schr dinger-Poisson Systems

HAO Cheng-Chun, XIAO Ling   

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
  • Received:2005-01-25 Online:2005-09-15

Abstract:

The bipolar(defocusing nonlinear) Schr dinger-Poisson system and quasilinear Schr dinger-Poisson equations are studied. The wellposedness, large time behavior and modified scattering theory is established for the Cauchy problem to the bipolar(defocusing nonlinear) Schr dinger-Poisson systems. The initia-l (Dirichlet) boundary problem for a high field version of the Schr dinger-Poisson equat ions, quas-i linear Schr dinger-Poisson equat ions, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effect ive potent ial in the Schr dinger equations on the unit cube are also discussed.

Key words: the bipolar defocusing nonlinear Schr dinger-Poisson system, the quas-i linear Schr dinger-Poisson systems, wellposedness of Cauchy problems, initial boundary value problem

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