| 关于Schrödinger-Poisson系统的研究（英文） |
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| 引用本文： | 郝成春,肖 玲.关于Schrödinger-Poisson系统的研究（英文）[J].中国科学院研究生院学报,2005,1(5):639-644. |
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| 作者姓名： | 郝成春 肖 玲 |
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| 作者单位： | HSIAO Ling（Academy of Mathematics and Systems Science, Chinese
Academy of Sciences, Beijing 100080, China） HAO Cheng-Chun（Academy of Mathematics and Systems Science, Chinese
Academy of Sciences, Beijing 100080, China） |
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| 摘 要： | 研究了双极(非线性) Schr"odinger-Poisson 系统和 拟线性Schr"odinger-Poisson 方程, 得到了双极 Schr"odinger-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"odinger-Poisson 方程的初边值问题整体解的存在唯一性.
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| 关 键 词： | 双极 Schr"odinger-Poisson系统 拟线性 Schr"odinger-Poisson方程 初值问题适定性 初边值问题. |
| 文章编号： | 1002-1175(2005)05-0639-06 |
| 修稿时间： | 2005年1月25日 |
The Study on Schrödinger-Poisson Systems |
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| HAO Cheng-Chun,HSIAO Ling.The Study on Schrödinger-Poisson Systems[J].Journal of the Graduate School of the Chinese Academy of Sciences,2005,1(5):639-644. |
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| Authors: | HAO Cheng-Chun HSIAO Ling |
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| Institution: | Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China |
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| Abstract: | 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. |
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| Keywords: | the bipolar defocusing nonlinear Schr¨odinger-Poisson system the quasi-linear Schr¨odinger-Poisson systems Wellposedness of Cauchy problems Initial boundary value problem |
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