关于Schrdinger-Poisson系统的研究(英文)

Studies on Schrdinger-Poisson Systems

研究了双极(非线性)Schrdinger-Poisson系统和拟线性Schrdinger-Poisson方程,得到了双极Schrdinger-Poisson系统的整体适定性及其修正散射理论,以及单位方体上的具有Dirichlet边值条件的拟线性Schrdinger-Poisson方程的初边值问题整体解的存在唯一性.

The bipolar（defocusing nonlinear）Schrfidinger-Poisson system and quasi-linear SchroedingerPoisson equations are studied. The wellposedness, large time behavior and modified scattering theory is established for the Cauchy problem to the bipolar（defocusing nonlinear）Schrfidinger-Poisson systems. The initial-（Dirichlet） boundary problem for a high field version of the SchrSdinger-Poisson equations, quasilinear Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant ＇and an effective potential in the Schroedinger equations on the unit cube are also discussed.