The Study on Schr dinger-Poisson Systems
关于Schr dinger-Poisson系统的研究（英文）

We studied the bipolar (defocusing nonlinear) Schr¨odinger-Poisson system and quasi-linear Schr¨odinger-Poisson equations. We constructed the wellposedness, large time behavior and modified scattering theory for Cauchy problem of the bipolar (defocusing nonlinear) Schr¨odinger-Poisson systems. We also discussed the initial-(Dirichlet) boundary problem for a high field version of the Schr¨odinger-Poisson equations, quasi-linear Schr¨odinger-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¨odinger equations on the unit cube.