Author(s): HSIAO Ling, HAO Cheng-Chun
Pages: 639-644
Year: 2005 Issue:  5
Journal: JOURNAL OF THE GRADUATE SCHOOL OF THE CHINESE ACADEMY OF SCIENCES
Keyword:  the bipolar defocusing nonlinear Schr(o)dinger-Poisson system; the quasi-linear Schr(o)dingerPoisson systems; wellposedness of Cauchy problems; initial boundary value problem;
Abstract: The bipolar(defocusing nonlinear)Schrodinger-Poisson system and quasi-linear Schr(o)dingerPoisson equations are studied. The wellposedness, large time behavior and modified scattering theory is established for the Cauchy problem to the bipolar(defocusing nonlinear)Schr(o)dinger-Poisson systems. The initial-(Dirichlet) boundary problem for a high field version of the Schr(o)dinger-Poisson equations, quasilinear Schr(o)dinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schr(o)dinger equations on the unit cube are also discussed.