Chinese Quarterly Journal of Mathematics ›› 2002, Vol. 16 ›› Issue (3): 18-23.

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Semi-classical Limit of Cubic Defocusing Nonlinear Schrödinger System

  

  1.  河南油田测井公司维也纳大学数学研究所 河南南阳473132维也纳91090 
  • Received:2001-07-16 Online:2002-09-30 Published:2024-04-26
  • About author:WANG Wei(1965-)‚male‚native of Xixia‚Henan‚a lecturer of Henan Oil Field‚M.S.D.‚engages in mining area geophysics and its application;WANG Shu(1968-)‚male‚native of Xixia‚Henan‚an associate professor of Henan University‚Ph.D.‚engages in nonlinear partial differential equations and its application.
  • Supported by:
    Supported by the National Youth Natural Science Foundation(10001034) of China;Supported by the
    FWF-Projekt “14876-MAT”“Fokker Planck and Mittlere-Feld-Gleichungen”(Austria).

Abstract: 全空间上非线性散焦立方薛定谔方程的半古典极限被证明。由量子力学中的薛定谔方程的解所定义的电子密度和电流密度当Planck常数趋于零时收敛于古典力学中的非线性可压缩欧拉方程的解。同时相应的Wigner函数在测度意义下收敛于非线性Viasov方程的解。这些结果的证明基于“改变”的Kinetic能量函数的估计和Wigner测度方法 

Key words: 非线性散焦薛定谔方程, 可压缩欧拉方程, 半古典极限, Wigner测度,  ,

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