Geometric Optics for One-Dimensional Schrodinger-Poisson System
Geometric Optics for One-Dimensional Schrodinger-Poisson System
摘要
这篇论文在一种尺寸考虑 Schroedinger 泊松系统的一个家庭，其起始的数据震荡以便一苛性出现。由使用 Lagrangianintegrals，作者在外面获得对答案的一致描述苛性、近苛性。
This paper considers a family of Schroedinger-Poisson system in one dimension, whose initial data oscillates so that a caustic appears. By using the Lagrangian integrals, the authors obtain a uniform description of the solution outside the caustic, and near the caustic.
关键词
几何光学
拉格朗日积分
振荡
腐蚀性
Schrodinger-Poisson, Geometric optics, Lagrangian integral
参考文献11
-
1Gasser, I., Lin, C. K. and Markowich, P. A., A review of dispersive limits of nonlinear Schroedinger-type equations, Taiwan Residents J. Math., 4, 2000, 501-529.
-
2Markowich, P. A., Ringhofer, C. and Schmeiser, C., Semiconductor equation, Springer-Verlag, New York,1990.
-
3Liu, H. and Tadmor, E., Semiclassical limit of the nonlinear SchrSdinger-Poisson equation with subcritical initial data, Methods Appl. Anal., 9, 2002, 517-531.
-
4Engelberg, S., Liu, H. and Tadmor, E., Critical thresholds in Euler-Poisson equations, Indiana Univ. Math.J., 50, Special Issue, 2001.
-
5Zhang, P., Zhen, Y. X. and Mauser, N. J., The Limit from Schroedinger-Poisson to Valsov-Poisson with general data in one dimension, Comm. Pure Appl. Math., 55, 2002, 582-632.
-
6Zhang, P., Winger measure and the semiclassical limit of Schroedinger-Poisson equations, SIAM J. Math.Anal., 34, 2003, 700-718.
-
7Caries, R., Geometric optics with caustic crossing for some nonlinear Schroedinger equations, Indiana Univ.Math. J., 49, 2000, 475-551.
-
8Duistermaat, J. J., Oscillatory integrals, Lagrangian immersions and unfolding of singularities, Comm.Pure Appl. Math., 27, 1974, 207-281.
-
9Joly, J. L., Métivier, G. and Rauch, J., Caustic for dissipative semilinear oscillations, Memoirs of A. M. S.,144(685), 2000, viii+72.
-
10Joly, J. L., Métivier, G. and Rauch, J., Nonlinear oscillations beyond caustics, Comm. Pure Appl. Math.,49, 1996, 443-527.
-
1肖玲,李海梁,杨彤,邹晨.COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R^3[J].Acta Mathematica Scientia,2011,31(6):2169-2194. 被引量：1
-
2郑森林,林强.分析原子干涉仪的矩阵方法[J].光学学报,2005,25(6):860-864. 被引量：3
-
3丁凌,孟义杰,张丹丹.R^3上的一类非齐次薛定谔-泊松系统解的存在唯一性[J].重庆工商大学学报（自然科学版）,2013,30(9):6-9.
-
4高付清.独立随机游动Poisson系统的中偏差[J].数学杂志,1996,16(2):133-136.
-
5崔国忠,宋锦萍.GLOBAL EXISTENCE OF SMOOTH SOLUTION FOR BOLTZMANN-POISSON SYSTEM WITH SMALL DATA[J].Acta Mathematica Scientia,2000,20(2):189-198.
-
6张金玲,熊丽华.一类非齐次薛定谔-泊松系统解的存在唯一性[J].湖北文理学院学报,2013,34(5):5-7.
-
7Guy Mtivier,Jeffrey Rauch.INVARIANCE AND STABILITY OF THE PROFILE EQUATIONS OF GEOMETRIC OPTICS[J].Acta Mathematica Scientia,2011,31(6):2141-2158.
-
8丁凌,庄常陵.一类推广的薛定谔—泊松系统的可解性[J].重庆工商大学学报（自然科学版）,2015,32(5):43-48.
-
9陈琼蕾,章志飞.GEOMETRIC OPTICS FOR 3D-HARTREE-TYPE EQUATION WITH COULOMB POTENTIAL[J].Acta Mathematica Scientia,2006,26(4):646-654.
-
10肖氏武,丁凌.一类推广的临界增长非线性薛定谔-泊松系统的不可解性[J].湖北文理学院学报,2014,35(11):5-7.
